एक वर्ग की भुजा \(\sqrt{7}\) इकाई है। उसका परिमाप किस प्रकार की संख्या होगा?
The side of a square is \(\sqrt{7}\) units. What type of number will its perimeter be?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C पूर्णांक / Integer
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय संख्या / Irrational number
Step 1
Concept
The perimeter is \(4\sqrt{7}\) and \(\sqrt{7}\) is irrational. A non-zero rational multiplier keeps irrationality.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय संख्या / Irrational number. The perimeter is \(4\sqrt{7}\) and \(\sqrt{7}\) is irrational. A non-zero rational multiplier keeps irrationality.
Step 3
Exam Tip
परिमाप \(4\sqrt{7}\) होगा और \(\sqrt{7}\) अपरिमेय है। शून्येतर परिमेय गुणक से अपरिमेयता बनी रहती है।
Login to save your score, XP, coins and progress. Login
किस दशमलव से अपरिमेय संख्या पहचानी जा सकती है?
Which decimal form can identify an irrational number?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A सांत दशमलव / Terminating decimal
B असांत अनावर्ती दशमलव / Non-terminating non-repeating decimal
C आवर्ती दशमलव / Repeating decimal
D पूर्णांक दशमलव / Integer decimal
Explanation opens after your attempt
Correct Answer
B. असांत अनावर्ती दशमलव / Non-terminating non-repeating decimal
Step 1
Concept
An irrational number has a non-terminating and non-repeating decimal. In exams check the repeating part carefully.
Step 2
Why this answer is correct
The correct answer is B. असांत अनावर्ती दशमलव / Non-terminating non-repeating decimal. An irrational number has a non-terminating and non-repeating decimal. In exams check the repeating part carefully.
Step 3
Exam Tip
अपरिमेय संख्या का दशमलव असांत और अनावर्ती होता है। परीक्षा में दोहराने वाले भाग को ध्यान से देखें।
Login to save your score, XP, coins and progress. Login
यदि किसी वर्ग का क्षेत्रफल (11) वर्ग इकाई है तो उसकी भुजा किस प्रकार की संख्या होगी?
If the area of a square is (11) square units then what type of number will its side be?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय संख्या / Rational number
B पूर्णांक / Integer
C सांत दशमलव / Terminating decimal
D अपरिमेय संख्या / Irrational number
Explanation opens after your attempt
Correct Answer
D. अपरिमेय संख्या / Irrational number
Step 1
Concept
The side will be \(\sqrt{11}\) and (11) is not a perfect square. So \(\sqrt{11}\) is irrational.
Step 2
Why this answer is correct
The correct answer is D. अपरिमेय संख्या / Irrational number. The side will be \(\sqrt{11}\) and (11) is not a perfect square. So \(\sqrt{11}\) is irrational.
Step 3
Exam Tip
भुजा \(\sqrt{11}\) होगी और (11) पूर्ण वर्ग नहीं है। इसलिए \(\sqrt{11}\) अपरिमेय है।
Login to save your score, XP, coins and progress. Login
दशमलव \(2.5050050005\ldots\) किस प्रकार की संख्या है?
What type of number is the decimal \(2.5050050005\ldots\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
It has no fixed repetition so it is irrational. Do not mistake a non-repeating pattern for a repeating one.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. It has no fixed repetition so it is irrational. Do not mistake a non-repeating pattern for a repeating one.
Step 3
Exam Tip
इसमें निश्चित दोहराव नहीं है इसलिए यह अपरिमेय है। अनावर्ती पैटर्न को आवर्ती मानने की गलती न करें।
Login to save your score, XP, coins and progress. Login
\(\sqrt{121}\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(\sqrt{121}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A यह अपरिमेय है / It is irrational
B यह परिमेय है / It is rational
C यह अनिर्धारित है / It is undefined
D यह ऋणात्मक है / It is negative
Explanation opens after your attempt
Correct Answer
B. यह परिमेय है / It is rational
Step 1
Concept
\(\sqrt{121}=11\) so it is rational. The square root of a perfect square is an integer.
Step 2
Why this answer is correct
The correct answer is B. यह परिमेय है / It is rational. \(\sqrt{121}=11\) so it is rational. The square root of a perfect square is an integer.
Step 3
Exam Tip
\(\sqrt{121}=11\) है इसलिए यह परिमेय है। पूर्ण वर्ग का वर्गमूल पूर्णांक होता है।
Login to save your score, XP, coins and progress. Login
इनमें से कौन-सा वर्गमूल अपरिमेय नहीं है?
Which square root is not irrational?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{31}\)
B \(\sqrt{40}\)
C \(\sqrt{64}\)
D \(\sqrt{72}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{64}\)
Step 1
Concept
\(\sqrt{64}=8\) so it is rational. Square roots of perfect squares are not irrational.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{64}\). \(\sqrt{64}=8\) so it is rational. Square roots of perfect squares are not irrational.
Step 3
Exam Tip
\(\sqrt{64}=8\) इसलिए यह परिमेय है। पूर्ण वर्गों के वर्गमूल अपरिमेय नहीं होते।
Login to save your score, XP, coins and progress. Login
यदि \(x=\sqrt{6}\) है तो (2x) किस प्रकार की संख्या है?
If \(x=\sqrt{6}\), what type of number is (2x)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय / Rational
B पूर्णांक / Integer
C अपरिमेय / Irrational
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
C. अपरिमेय / Irrational
Step 1
Concept
\(2x=2\sqrt{6}\), which is irrational. Multiplication by a non-zero rational keeps irrationality.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय / Irrational. \(2x=2\sqrt{6}\), which is irrational. Multiplication by a non-zero rational keeps irrationality.
Step 3
Exam Tip
\(2x=2\sqrt{6}\) होगा जो अपरिमेय है। शून्येतर परिमेय से गुणा करने पर अपरिमेयता बनी रहती है।
Login to save your score, XP, coins and progress. Login
\(\sqrt{3}\times\sqrt{27}\) का मान क्या है?
What is the value of \(\sqrt{3}\times\sqrt{27}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (9)
B \(\sqrt{30}\)
C \(3\sqrt{3}\)
D \(\sqrt{81}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). The product of two irrationals can be rational.
Step 2
Why this answer is correct
The correct answer is A. (9). \(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). The product of two irrationals can be rational.
Step 3
Exam Tip
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\) होता है। दो अपरिमेयों का गुणनफल परिमेय हो सकता है।
Login to save your score, XP, coins and progress. Login
कौन-सी संख्या \(\sqrt{10}\) और \(\sqrt{11}\) के बीच निश्चित रूप से है?
Which number definitely lies between \(\sqrt{10}\) and \(\sqrt{11}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3)
B \(\sqrt{10.5}\)
C (4)
D \(\sqrt{9}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{10.5}\)
Step 1
Concept
Since (10<10.5<11), \(\sqrt{10.5}\) lies between them. Compare square roots using the numbers inside.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{10.5}\). Since (10<10.5<11), \(\sqrt{10.5}\) lies between them. Compare square roots using the numbers inside.
Step 3
Exam Tip
क्योंकि (10<10.5<11), इसलिए \(\sqrt{10.5}\) दोनों के बीच है। वर्गमूल की तुलना अंदर की संख्याओं से करें।
Login to save your score, XP, coins and progress. Login
\(\sqrt{48}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{48}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(6\sqrt{2}\)
B \(8\sqrt{3}\)
C \(4\sqrt{3}\)
D (12)
Explanation opens after your attempt
Correct Answer
C. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}\). Take the perfect-square factor outside.
Step 2
Why this answer is correct
The correct answer is C. \(4\sqrt{3}\). \(\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}\). Take the perfect-square factor outside.
Step 3
Exam Tip
\(\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}\) है। पूर्ण वर्ग गुणनखंड बाहर निकालें।
Login to save your score, XP, coins and progress. Login
यदि \(a=\sqrt{5}\) है तो \(a^2\) किस प्रकार की संख्या है?
If \(a=\sqrt{5}\), what type of number is \(a^2\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A अपरिमेय / Irrational
B परिमेय / Rational
C अनिर्धारित / Undefined
D ऋणात्मक / Negative
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Step 1
Concept
(a-2 =\(\sqrt{5}\)2 =5), so it is rational. The square of an irrational can sometimes be rational.
Step 2
Why this answer is correct
The correct answer is B. परिमेय / Rational. (a-2 =\(\sqrt{5}\)2 =5), so it is rational. The square of an irrational can sometimes be rational.
Step 3
Exam Tip
(a-2 =\(\sqrt{5}\)2 =5) है इसलिए यह परिमेय है। अपरिमेय का वर्ग कभी-कभी परिमेय होता है।
Login to save your score, XP, coins and progress. Login
\(\frac{\sqrt{45}}{\sqrt{5}}\) का मान क्या है?
What is the value of \(\frac{\sqrt{45}}{\sqrt{5}}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{40}\)
B (5)
C (3)
D \(\sqrt{50}\)
Explanation opens after your attempt
Step 1
Concept
\(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3\). After simplification the result can be rational.
Step 2
Why this answer is correct
The correct answer is C. (3). \(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3\). After simplification the result can be rational.
Step 3
Exam Tip
\(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3\) है। सरलीकरण के बाद परिणाम परिमेय हो सकता है।
Login to save your score, XP, coins and progress. Login
\(\sqrt[3]{27}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt[3]{27}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A अपरिमेय / Irrational
B परिमेय / Rational
C अनावर्ती दशमलव / Non-repeating decimal
D अनिर्धारित / Undefined
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Step 1
Concept
\(\sqrt[3]{27}=3\) so it is rational. The cube root of a perfect cube is rational.
Step 2
Why this answer is correct
The correct answer is B. परिमेय / Rational. \(\sqrt[3]{27}=3\) so it is rational. The cube root of a perfect cube is rational.
Step 3
Exam Tip
\(\sqrt[3]{27}=3\) है इसलिए यह परिमेय है। पूर्ण घन का घनमूल परिमेय होता है।
Login to save your score, XP, coins and progress. Login
\(\sqrt[3]{5}\) के बारे में सही कथन चुनिए।
Choose the correct statement about \(\sqrt[3]{5}\).
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A यह परिमेय है / It is rational
B यह पूर्णांक है / It is an integer
C यह अपरिमेय है / It is irrational
D यह शून्य है / It is zero
Explanation opens after your attempt
Correct Answer
C. यह अपरिमेय है / It is irrational
Step 1
Concept
(5) is not a perfect cube so \(\sqrt[3]{5}\) is irrational. In cube roots check perfect cubes.
Step 2
Why this answer is correct
The correct answer is C. यह अपरिमेय है / It is irrational. (5) is not a perfect cube so \(\sqrt[3]{5}\) is irrational. In cube roots check perfect cubes.
Step 3
Exam Tip
(5) पूर्ण घन नहीं है इसलिए \(\sqrt[3]{5}\) अपरिमेय है। घनमूल में पूर्ण घन देखना चाहिए।
Login to save your score, XP, coins and progress. Login
इनमें से कौन-सा (1) और (3) के बीच अपरिमेय है?
Which of these is irrational between (1) and (3)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{9}\)
B \(\sqrt{5}\)
C (2)
D (2.5)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{5}\) lies between (1) and (3) and is irrational. Estimate using nearby perfect squares.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{5}\). \(\sqrt{5}\) lies between (1) and (3) and is irrational. Estimate using nearby perfect squares.
Step 3
Exam Tip
\(\sqrt{5}\) का मान (1) और (3) के बीच है और यह अपरिमेय है। निकट पूर्ण वर्गों से अनुमान लगाएं।
Login to save your score, XP, coins and progress. Login
\(6-\sqrt{2}\) किस प्रकार की संख्या है?
What type of number is \(6-\sqrt{2}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय / Rational
B पूर्णांक / Integer
C अपरिमेय / Irrational
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
C. अपरिमेय / Irrational
Step 1
Concept
Subtracting irrational \(\sqrt{2}\) from rational (6) gives an irrational number. The irrational part does not disappear.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय / Irrational. Subtracting irrational \(\sqrt{2}\) from rational (6) gives an irrational number. The irrational part does not disappear.
Step 3
Exam Tip
परिमेय (6) में से अपरिमेय \(\sqrt{2}\) घटाने पर अपरिमेय संख्या मिलती है। अपरिमेय भाग खत्म नहीं होता।
Login to save your score, XP, coins and progress. Login
\(\sqrt{7}+\sqrt{7}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{7}+\sqrt{7}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2\sqrt{7}\)
B \(\sqrt{14}\)
C (7)
D (14)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
Adding like radicals gives \(2\sqrt{7}\). It is irrational because \(\sqrt{7}\) remains.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{7}\). Adding like radicals gives \(2\sqrt{7}\). It is irrational because \(\sqrt{7}\) remains.
Step 3
Exam Tip
समान मूलों को जोड़ने पर \(2\sqrt{7}\) मिलता है। यह अपरिमेय है क्योंकि \(\sqrt{7}\) बचता है।
Login to save your score, XP, coins and progress. Login
\(\sqrt{12}+\sqrt{75}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{12}+\sqrt{75}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(7\sqrt{3}\)
B \(9\sqrt{3}\)
C \(5\sqrt{3}\)
D \(\sqrt{87}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\), so the sum is \(7\sqrt{3}\). Simplify both radicals first.
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\), so the sum is \(7\sqrt{3}\). Simplify both radicals first.
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\), इसलिए योग \(7\sqrt{3}\) है। पहले दोनों मूल सरल करें।
Login to save your score, XP, coins and progress. Login
\(\sqrt{80}-\sqrt{45}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{80}-\sqrt{45}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{35}\)
B \(5\sqrt{5}\)
C \(\sqrt{5}\)
D \(4\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so the difference is \(\sqrt{5}\). Subtract like radicals.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{5}\). \(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so the difference is \(\sqrt{5}\). Subtract like radicals.
Step 3
Exam Tip
\(\sqrt{80}=4\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\), इसलिए अंतर \(\sqrt{5}\) है। समान मूलों को घटाएं।
Login to save your score, XP, coins and progress. Login
\(\frac{5}{\sqrt{5}}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\frac{5}{\sqrt{5}}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(5\sqrt{5}\)
B \(\sqrt{5}\)
C (1)
D (25)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{5}\)
Step 1
Concept
\(\frac{5}{\sqrt{5}}=\sqrt{5}\). Simplify carefully when the denominator has a radical.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{5}\). \(\frac{5}{\sqrt{5}}=\sqrt{5}\). Simplify carefully when the denominator has a radical.
Step 3
Exam Tip
\(\frac{5}{\sqrt{5}}=\sqrt{5}\) होता है। हर में मूल हो तो सरलीकरण ध्यान से करें।
Login to save your score, XP, coins and progress. Login
\(\frac{1}{\sqrt{3}}\) को हर में मूल हटाकर कैसे लिखा जा सकता है?
How can \(\frac{1}{\sqrt{3}}\) be written after removing the radical from the denominator?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\frac{\sqrt{3}}{3}\)
B \(\frac{3}{\sqrt{3}}\)
C \(3\sqrt{3}\)
D \(\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\sqrt{3}}{3}\)
Step 1
Concept
Multiplying \(\frac{1}{\sqrt{3}}\) by \(\frac{\sqrt{3}}{\sqrt{3}}\) gives \(\frac{\sqrt{3}}{3}\). This is called rationalising the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\sqrt{3}}{3}\). Multiplying \(\frac{1}{\sqrt{3}}\) by \(\frac{\sqrt{3}}{\sqrt{3}}\) gives \(\frac{\sqrt{3}}{3}\). This is called rationalising the denominator.
Step 3
Exam Tip
\(\frac{1}{\sqrt{3}}\) को \(\frac{\sqrt{3}}{\sqrt{3}}\) से गुणा करने पर \(\frac{\sqrt{3}}{3}\) मिलता है। इसे हर का परिमेयकरण कहते हैं।
Login to save your score, XP, coins and progress. Login
कौन-सा विकल्प परिमेय संख्या है?
Which option is a rational number?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{29}\)
B \(\sqrt{2}+1\)
C \(\pi\)
D \(0.454545\ldots\)
Explanation opens after your attempt
Correct Answer
D. \(0.454545\ldots\)
Step 1
Concept
\(0.454545\ldots\) is repeating so it is rational. A repeating decimal can be converted into a fraction.
Step 2
Why this answer is correct
The correct answer is D. \(0.454545\ldots\). \(0.454545\ldots\) is repeating so it is rational. A repeating decimal can be converted into a fraction.
Step 3
Exam Tip
\(0.454545\ldots\) आवर्ती दशमलव है इसलिए परिमेय है। आवर्ती दशमलव को भिन्न में बदला जा सकता है।
Login to save your score, XP, coins and progress. Login
\(\pi+2\) किस प्रकार की संख्या है?
What type of number is \(\pi+2\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\pi\) is irrational and (2) is rational, so the sum is irrational. Do not treat \(\pi\) as equal to (22/7).
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(\pi\) is irrational and (2) is rational, so the sum is irrational. Do not treat \(\pi\) as equal to (22/7).
Step 3
Exam Tip
\(\pi\) अपरिमेय है और (2) परिमेय है, इसलिए योग अपरिमेय है। \(\pi\) को (22/7) के बराबर न मानें।
Login to save your score, XP, coins and progress. Login
(22/7) के बारे में सही कथन कौन-सा है?
Which statement is correct about (22/7)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A यह \(\pi\) का निकट मान है / It is an approximation of \(\pi\)
B यह अपरिमेय है / It is irrational
C यह \(\pi\) के बिल्कुल बराबर है / It is exactly equal to \(\pi\)
D यह पूर्णांक है / It is an integer
Explanation opens after your attempt
Correct Answer
A. यह \(\pi\) का निकट मान है / It is an approximation of \(\pi\)
Step 1
Concept
(22/7) is rational and an approximation of \(\pi\). Do not treat an approximation as exact equality.
Step 2
Why this answer is correct
The correct answer is A. यह \(\pi\) का निकट मान है / It is an approximation of \(\pi\). (22/7) is rational and an approximation of \(\pi\). Do not treat an approximation as exact equality.
Step 3
Exam Tip
(22/7) परिमेय है और \(\pi\) का निकट मान है। निकट मान को वास्तविक बराबरी न समझें।
Login to save your score, XP, coins and progress. Login
यदि किसी संख्या का दशमलव \(4.10110111011110\ldots\) है, तो वह कैसी है?
If a number has decimal \(4.10110111011110\ldots\), what is it?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D सांत / Terminating
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
This decimal is non-terminating and non-repeating so it is irrational. There is no fixed repeating block.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. This decimal is non-terminating and non-repeating so it is irrational. There is no fixed repeating block.
Step 3
Exam Tip
यह दशमलव असांत और अनावर्ती है इसलिए अपरिमेय है। निश्चित दोहराने वाला ब्लॉक नहीं है।
Login to save your score, XP, coins and progress. Login
\(\sqrt{\frac{16}{25}}\) किसके बराबर है?
What is \(\sqrt{\frac{16}{25}}\) equal to?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\frac{8}{5}\)
B \(\frac{4}{5}\)
C \(\frac{16}{25}\)
D \(\frac{5}{4}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{4}{5}\)
Step 1
Concept
\(\sqrt{\frac{16}{25}}=\frac{4}{5}\), so it is rational. Both numerator and denominator are perfect squares.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{4}{5}\). \(\sqrt{\frac{16}{25}}=\frac{4}{5}\), so it is rational. Both numerator and denominator are perfect squares.
Step 3
Exam Tip
\(\sqrt{\frac{16}{25}}=\frac{4}{5}\) है इसलिए यह परिमेय है। अंश और हर दोनों पूर्ण वर्ग हैं।
Login to save your score, XP, coins and progress. Login
\(\sqrt{\frac{7}{4}}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{\frac{7}{4}}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{\frac{7}{4}}=\frac{\sqrt{7}}{2}\) and \(\sqrt{7}\) is irrational. Check perfect squares even in fractions.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(\sqrt{\frac{7}{4}}=\frac{\sqrt{7}}{2}\) and \(\sqrt{7}\) is irrational. Check perfect squares even in fractions.
Step 3
Exam Tip
\(\sqrt{\frac{7}{4}}=\frac{\sqrt{7}}{2}\) है और \(\sqrt{7}\) अपरिमेय है। भिन्न में भी पूर्ण वर्ग जाँचें।
Login to save your score, XP, coins and progress. Login
\(10\sqrt{2}\div5\) का सरल रूप क्या है?
What is the simplified form of \(10\sqrt{2}\div5\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2\sqrt{2}\)
B \(5\sqrt{2}\)
C \(10\sqrt{10}\)
D (\sqrt{2} / 5)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{2}\)
Step 1
Concept
\(10\sqrt{2}\div5=2\sqrt{2}\), which is irrational. Simplify the numerical coefficient separately.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{2}\). \(10\sqrt{2}\div5=2\sqrt{2}\), which is irrational. Simplify the numerical coefficient separately.
Step 3
Exam Tip
\(10\sqrt{2}\div5=2\sqrt{2}\) है जो अपरिमेय है। संख्यात्मक गुणांक को अलग सरल करें।
Login to save your score, XP, coins and progress. Login
\(-3\sqrt{11}\) किस प्रकार की संख्या है?
What type of number is \(-3\sqrt{11}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय / Rational
B अपरिमेय / Irrational
C प्राकृतिक / Natural
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{11}\) is irrational and (-3) is a non-zero rational multiplier. So the result is irrational.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(\sqrt{11}\) is irrational and (-3) is a non-zero rational multiplier. So the result is irrational.
Step 3
Exam Tip
\(\sqrt{11}\) अपरिमेय है और (-3) शून्येतर परिमेय गुणक है। इसलिए परिणाम अपरिमेय है।
Login to save your score, XP, coins and progress. Login
\(\sqrt{13}\) का विपरीत संख्या कौन-सी है?
What is the additive inverse of \(\sqrt{13}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\frac{1}{\sqrt{13}}\)
B \(-\sqrt{13}\)
C (13)
D (-13)
Explanation opens after your attempt
Correct Answer
B. \(-\sqrt{13}\)
Step 1
Concept
The additive inverse gives (0) when added, so \(-\sqrt{13}\) is correct. It is also irrational.
Step 2
Why this answer is correct
The correct answer is B. \(-\sqrt{13}\). The additive inverse gives (0) when added, so \(-\sqrt{13}\) is correct. It is also irrational.
Step 3
Exam Tip
विपरीत संख्या जोड़ने पर (0) देती है, इसलिए \(-\sqrt{13}\) सही है। यह भी अपरिमेय है।
Login to save your score, XP, coins and progress. Login
\(\sqrt{13}\) का व्युत्क्रम कौन-सा है?
Which is the reciprocal of \(\sqrt{13}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(-\sqrt{13}\)
B \(\frac{1}{\sqrt{13}}\)
C (13)
D \(\sqrt{13}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{\sqrt{13}}\)
Step 1
Concept
The reciprocal is the number whose product gives (1). \(\sqrt{13}\times\frac{1}{\sqrt{13}}=1\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{\sqrt{13}}\). The reciprocal is the number whose product gives (1). \(\sqrt{13}\times\frac{1}{\sqrt{13}}=1\).
Step 3
Exam Tip
व्युत्क्रम वह है जिसका गुणनफल (1) देता है। \(\sqrt{13}\times\frac{1}{\sqrt{13}}=1\) होता है।
Login to save your score, XP, coins and progress. Login
(\(\sqrt{2}+1\)-\sqrt{2}) का मान क्या है?
What is the value of (\(\sqrt{2}+1\)-\sqrt{2})?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A अपरिमेय \(\sqrt{2}\) / Irrational \(\sqrt{2}\)
B परिमेय (1) / Rational (1)
C परिमेय (2) / Rational (2)
D अपरिमेय \(1+\sqrt{2}\) / Irrational \(1+\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
B. परिमेय (1) / Rational (1)
Step 1
Concept
The \(\sqrt{2}\) terms cancel and the value is (1). Sometimes irrational terms can cancel to give a rational result.
Step 2
Why this answer is correct
The correct answer is B. परिमेय (1) / Rational (1). The \(\sqrt{2}\) terms cancel and the value is (1). Sometimes irrational terms can cancel to give a rational result.
Step 3
Exam Tip
\(\sqrt{2}\) के पद कट जाते हैं और मान (1) है। कभी-कभी अपरिमेय पद हटकर परिमेय परिणाम दे सकते हैं।
Login to save your score, XP, coins and progress. Login
(\(\sqrt{6}+2\)\(\sqrt{6}-2\)) का मान क्या है?
What is the value of (\(\sqrt{6}+2\)\(\sqrt{6}-2\))?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B \(\sqrt{6}\)
C (10)
D \(4\sqrt{6}\)
Explanation opens after your attempt
Step 1
Concept
This is ((a+b)(a-b)=a-2 -b-2 ), so the value is (6-4=2). Conjugates can make the result rational.
Step 2
Why this answer is correct
The correct answer is A. (2). This is ((a+b)(a-b)=a-2 -b-2 ), so the value is (6-4=2). Conjugates can make the result rational.
Step 3
Exam Tip
यह ((a+b)(a-b)=a-2 -b-2 ) है, इसलिए मान (6-4=2) है। संयुग्मी रूप परिणाम को परिमेय बना सकता है।
Login to save your score, XP, coins and progress. Login
(\(\sqrt{5}+1\)\(\sqrt{5}+1\)) का प्रसार कौन-सा है?
Which is the expansion of (\(\sqrt{5}+1\)\(\sqrt{5}+1\))?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(6+2\sqrt{5}\)
B \(5+\sqrt{5}\)
C (10)
D \(4+2\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(6+2\sqrt{5}\)
Step 1
Concept
(\(\sqrt{5}+1\)2 =5+2\sqrt{5}+1=6+2\sqrt{5}). Do not forget the middle term.
Step 2
Why this answer is correct
The correct answer is A. \(6+2\sqrt{5}\). (\(\sqrt{5}+1\)2 =5+2\sqrt{5}+1=6+2\sqrt{5}). Do not forget the middle term.
Step 3
Exam Tip
(\(\sqrt{5}+1\)2 =5+2\sqrt{5}+1=6+2\sqrt{5}) है। मध्य पद भूलना नहीं चाहिए।
Login to save your score, XP, coins and progress. Login
\(\sqrt{2}\) और \(\sqrt{3}\) की तुलना में कौन-सा कथन सही है?
Which statement is correct when comparing \(\sqrt{2}\) and \(\sqrt{3}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{2}>\sqrt{3}\)
B \(\sqrt{2}=\sqrt{3}\)
C \(\sqrt{2}<\sqrt{3}\)
D दोनों परिमेय हैं / Both are rational
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{2}<\sqrt{3}\)
Step 1
Concept
Since (2<3), \(\sqrt{2}<\sqrt{3}\). For positive square roots compare the numbers inside.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{2}<\sqrt{3}\). Since (2<3), \(\sqrt{2}<\sqrt{3}\). For positive square roots compare the numbers inside.
Step 3
Exam Tip
क्योंकि (2<3), इसलिए \(\sqrt{2}<\sqrt{3}\)। धनात्मक संख्याओं के वर्गमूल में अंदर की संख्या की तुलना करें।
Login to save your score, XP, coins and progress. Login
\(\sqrt{17}\) किन दो पूर्णांकों के बीच है?
Between which two integers does \(\sqrt{17}\) lie?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3) और (4) / (3) and (4)
B (4) और (5) / (4) and (5)
C (5) और (6) / (5) and (6)
D (8) और (9) / (8) and (9)
Explanation opens after your attempt
Correct Answer
B. (4) और (5) / (4) and (5)
Step 1
Concept
Since (16<17<25), \(4<\sqrt{17}<5\). Use nearby perfect squares to decide bounds.
Step 2
Why this answer is correct
The correct answer is B. (4) और (5) / (4) and (5). Since (16<17<25), \(4<\sqrt{17}<5\). Use nearby perfect squares to decide bounds.
Step 3
Exam Tip
क्योंकि (16<17<25), इसलिए \(4<\sqrt{17}<5\)। निकट पूर्ण वर्गों से सीमा तय करें।
Login to save your score, XP, coins and progress. Login
संख्या रेखा पर \(\sqrt{2}\) को किस त्रिभुज से बनाया जा सकता है?
On the number line, \(\sqrt{2}\) can be constructed using which triangle?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A समकोण त्रिभुज जिसकी भुजाएँ (1) और (1) हों / Right triangle with legs (1) and (1)
B समबाहु त्रिभुज जिसकी भुजा (2) हो / Equilateral triangle with side (2)
C त्रिभुज जिसकी भुजाएँ (2) और (2) हों / Triangle with sides (2) and (2)
D रेखा खंड जिसकी लंबाई (3) हो / Line segment of length (3)
Explanation opens after your attempt
Correct Answer
A. समकोण त्रिभुज जिसकी भुजाएँ (1) और (1) हों / Right triangle with legs (1) and (1)
Step 1
Concept
In a right triangle, the hypotenuse is \(\sqrt{1^2+1^2}=\sqrt{2}\). Understand construction using Pythagoras theorem.
Step 2
Why this answer is correct
The correct answer is A. समकोण त्रिभुज जिसकी भुजाएँ (1) और (1) हों / Right triangle with legs (1) and (1). In a right triangle, the hypotenuse is \(\sqrt{1^2+1^2}=\sqrt{2}\). Understand construction using Pythagoras theorem.
Step 3
Exam Tip
समकोण त्रिभुज में कर्ण \(\sqrt{1^2+1^2}=\sqrt{2}\) होता है। पाइथागोरस प्रमेय से निर्माण समझें।
Login to save your score, XP, coins and progress. Login
किस संख्या को संख्या रेखा पर ठीक-ठीक दिखाया जा सकता है?
Which number can be represented exactly on the number line?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A केवल परिमेय संख्या / Only rational number
B केवल पूर्णांक / Only integers
C परिमेय और अपरिमेय दोनों / Both rational and irrational numbers
D केवल प्राकृतिक संख्या / Only natural numbers
Explanation opens after your attempt
Correct Answer
C. परिमेय और अपरिमेय दोनों / Both rational and irrational numbers
Step 1
Concept
The number line represents real numbers, including both rational and irrational numbers. Irrationals can be constructed geometrically.
Step 2
Why this answer is correct
The correct answer is C. परिमेय और अपरिमेय दोनों / Both rational and irrational numbers. The number line represents real numbers, including both rational and irrational numbers. Irrationals can be constructed geometrically.
Step 3
Exam Tip
संख्या रेखा पर वास्तविक संख्याएँ दिखाई जाती हैं जिनमें परिमेय और अपरिमेय दोनों शामिल हैं। अपरिमेयों का निर्माण ज्यामिति से किया जा सकता है।
Login to save your score, XP, coins and progress. Login
यदि एक वर्ग की भुजा \(\sqrt{3}\) इकाई है तो उसका क्षेत्रफल क्या होगा?
If the side of a square is \(\sqrt{3}\) units, what will be its area?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3) वर्ग इकाई / (3) square units
B \(\sqrt{3}\) वर्ग इकाई / \(\sqrt{3}\) square units
C (6) वर्ग इकाई / (6) square units
D (9) वर्ग इकाई / (9) square units
Explanation opens after your attempt
Correct Answer
A. (3) वर्ग इकाई / (3) square units
Step 1
Concept
The area is (\(\sqrt{3}\)2 =3). A square with irrational side can have rational area.
Step 2
Why this answer is correct
The correct answer is A. (3) वर्ग इकाई / (3) square units. The area is (\(\sqrt{3}\)2 =3). A square with irrational side can have rational area.
Step 3
Exam Tip
क्षेत्रफल (\(\sqrt{3}\)2 =3) है। अपरिमेय भुजा का क्षेत्रफल परिमेय हो सकता है।
Login to save your score, XP, coins and progress. Login
किस संख्या का वर्ग (19) है और वह धनात्मक है?
Which number has square (19) and is positive?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{19}\)
B (19)
C (361)
D \(-\sqrt{19}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{19}\)
Step 1
Concept
The positive number is \(\sqrt{19}\) because (\(\sqrt{19}\)2 =19). Since (19) is not a perfect square, it is irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{19}\). The positive number is \(\sqrt{19}\) because (\(\sqrt{19}\)2 =19). Since (19) is not a perfect square, it is irrational.
Step 3
Exam Tip
धनात्मक संख्या \(\sqrt{19}\) है क्योंकि (\(\sqrt{19}\)2 =19)। (19) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है।
Login to save your score, XP, coins and progress. Login
\(\sqrt{2}\) का दशमलव प्रसार कैसा होता है?
What is the decimal expansion of \(\sqrt{2}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A सांत / Terminating
B आवर्ती / Repeating
C असांत अनावर्ती / Non-terminating non-repeating
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
C. असांत अनावर्ती / Non-terminating non-repeating
Step 1
Concept
\(\sqrt{2}\) is irrational so its decimal is non-terminating and non-repeating. Do not conclude from only a few decimal digits.
Step 2
Why this answer is correct
The correct answer is C. असांत अनावर्ती / Non-terminating non-repeating. \(\sqrt{2}\) is irrational so its decimal is non-terminating and non-repeating. Do not conclude from only a few decimal digits.
Step 3
Exam Tip
\(\sqrt{2}\) अपरिमेय है इसलिए इसका दशमलव असांत और अनावर्ती होता है। दशमलव के कुछ अंक देखकर निष्कर्ष न लगाएं।
Login to save your score, XP, coins and progress. Login
इनमें से कौन-सा कथन गलत है?
Which of the following statements is false?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A हर पूर्णांक परिमेय होता है / Every integer is rational
B हर सांत दशमलव परिमेय होता है / Every terminating decimal is rational
C हर अपरिमेय संख्या वास्तविक होती है / Every irrational number is real
D हर वास्तविक संख्या परिमेय होती है / Every real number is rational
Explanation opens after your attempt
Correct Answer
D. हर वास्तविक संख्या परिमेय होती है / Every real number is rational
Step 1
Concept
Every real number is not rational because irrational numbers are also real. The number system includes both types.
Step 2
Why this answer is correct
The correct answer is D. हर वास्तविक संख्या परिमेय होती है / Every real number is rational. Every real number is not rational because irrational numbers are also real. The number system includes both types.
Step 3
Exam Tip
हर वास्तविक संख्या परिमेय नहीं होती क्योंकि अपरिमेय संख्याएँ भी वास्तविक हैं। संख्या तंत्र में दोनों प्रकार शामिल हैं।
Login to save your score, XP, coins and progress. Login
इनमें से कौन-सा युग्म दोनों अपरिमेय संख्याओं का है?
Which pair contains two irrational numbers?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{4}\) और \(\sqrt{9}\) / \(\sqrt{4}\) and \(\sqrt{9}\)
B \(\sqrt{2}\) और \(\sqrt{5}\) / \(\sqrt{2}\) and \(\sqrt{5}\)
C (1 / 2) और \(\sqrt{16}\) / 2) and \(\sqrt{16}\)
D (0.75) और (3) / (0.75) and (3)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{2}\) और \(\sqrt{5}\) / \(\sqrt{2}\) and \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{2}\) and \(\sqrt{5}\) are both irrational because (2) and (5) are not perfect squares. Check each number separately.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{2}\) और \(\sqrt{5}\) / \(\sqrt{2}\) and \(\sqrt{5}\). \(\sqrt{2}\) and \(\sqrt{5}\) are both irrational because (2) and (5) are not perfect squares. Check each number separately.
Step 3
Exam Tip
\(\sqrt{2}\) और \(\sqrt{5}\) दोनों अपरिमेय हैं क्योंकि (2) और (5) पूर्ण वर्ग नहीं हैं। प्रत्येक संख्या को अलग जाँचें।
Login to save your score, XP, coins and progress. Login
\(\sqrt{28}+\sqrt{63}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{28}+\sqrt{63}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(5\sqrt{7}\)
B \(7\sqrt{5}\)
C \(13\sqrt{7}\)
D \(\sqrt{91}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{7}\)
Step 1
Concept
\(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{63}=3\sqrt{7}\), so the sum is \(5\sqrt{7}\). Add like radicals.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{7}\). \(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{63}=3\sqrt{7}\), so the sum is \(5\sqrt{7}\). Add like radicals.
Step 3
Exam Tip
\(\sqrt{28}=2\sqrt{7}\) और \(\sqrt{63}=3\sqrt{7}\), इसलिए योग \(5\sqrt{7}\) है। समान मूलों को जोड़ें।
Login to save your score, XP, coins and progress. Login
\(\sqrt{72}-\sqrt{8}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{72}-\sqrt{8}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2\sqrt{2}\)
B \(8\sqrt{2}\)
C \(\sqrt{64}\)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
D. \(4\sqrt{2}\)
Step 1
Concept
\(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the difference is \(4\sqrt{2}\). Simplify like radicals first.
Step 2
Why this answer is correct
The correct answer is D. \(4\sqrt{2}\). \(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the difference is \(4\sqrt{2}\). Simplify like radicals first.
Step 3
Exam Tip
\(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\), इसलिए अंतर \(4\sqrt{2}\) है। पहले समान मूलों को सरल करें।
Login to save your score, XP, coins and progress. Login
\(\frac{\sqrt{27}}{3}\) किसके बराबर है?
What is \(\frac{\sqrt{27}}{3}\) equal to?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(3\sqrt{3}\)
B \(\sqrt{3}\)
C (9)
D \(\frac{1}{\sqrt{3}}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\), so \(\frac{\sqrt{27}}{3}=\sqrt{3}\). The result is still irrational.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{3}\). \(\sqrt{27}=3\sqrt{3}\), so \(\frac{\sqrt{27}}{3}=\sqrt{3}\). The result is still irrational.
Step 3
Exam Tip
\(\sqrt{27}=3\sqrt{3}\) है, इसलिए \(\frac{\sqrt{27}}{3}=\sqrt{3}\) होता है। परिणाम अभी भी अपरिमेय है।
Login to save your score, XP, coins and progress. Login
यदि किसी धनात्मक संख्या का वर्ग (37) है, तो वह संख्या कौन-सी होगी?
If the square of a positive number is (37), which number is it?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{37}\)
B (37)
C \(-\sqrt{37}\)
D (74)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{37}\)
Step 1
Concept
The positive number is \(\sqrt{37}\) because (\(\sqrt{37}\)2 =37). Since (37) is not a perfect square, it is irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{37}\). The positive number is \(\sqrt{37}\) because (\(\sqrt{37}\)2 =37). Since (37) is not a perfect square, it is irrational.
Step 3
Exam Tip
धनात्मक संख्या \(\sqrt{37}\) है क्योंकि (\(\sqrt{37}\)2 =37)। (37) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है।
Login to save your score, XP, coins and progress. Login
दशमलव \(3.14114111411114\ldots\) किस प्रकार की संख्या है?
What type of number is the decimal \(3.14114111411114\ldots\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A सांत परिमेय / Terminating rational
B आवर्ती परिमेय / Repeating rational
C अपरिमेय / Irrational
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
C. अपरिमेय / Irrational
Step 1
Concept
This decimal has no fixed repeating block. So it is a non-terminating non-repeating decimal and an irrational number.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय / Irrational. This decimal has no fixed repeating block. So it is a non-terminating non-repeating decimal and an irrational number.
Step 3
Exam Tip
इस दशमलव में निश्चित दोहराने वाला खंड नहीं है। इसलिए यह असांत अनावर्ती दशमलव और अपरिमेय संख्या है।
Login to save your score, XP, coins and progress. Login
\(\sqrt{96}\) को सरल करने पर कौन-सा रूप मिलता है?
Which form is obtained after simplifying \(\sqrt{96}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(4\sqrt{6}\)
B \(6\sqrt{4}\)
C \(8\sqrt{3}\)
D \(16\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{6}\)
Step 1
Concept
\(\sqrt{96}=\sqrt{16\times6}=4\sqrt{6}\). Since \(\sqrt{6}\) remains, it is irrational.
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{6}\). \(\sqrt{96}=\sqrt{16\times6}=4\sqrt{6}\). Since \(\sqrt{6}\) remains, it is irrational.
Step 3
Exam Tip
\(\sqrt{96}=\sqrt{16\times6}=4\sqrt{6}\) है। \(\sqrt{6}\) बचने से यह अपरिमेय है।
Login to save your score, XP, coins and progress. Login
\(\sqrt{44}+\sqrt{99}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{44}+\sqrt{99}\)?
#number-systems
#irrational-numbers
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(5\sqrt{11}\)
B \(7\sqrt{11}\)
C \(11\sqrt{13}\)
D \(\sqrt{143}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{11}\)
Step 1
Concept
\(\sqrt{44}=2\sqrt{11}\) and \(\sqrt{99}=3\sqrt{11}\), so the sum is \(5\sqrt{11}\). Simplify before adding like radicals.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{11}\). \(\sqrt{44}=2\sqrt{11}\) and \(\sqrt{99}=3\sqrt{11}\), so the sum is \(5\sqrt{11}\). Simplify before adding like radicals.
Step 3
Exam Tip
\(\sqrt{44}=2\sqrt{11}\) और \(\sqrt{99}=3\sqrt{11}\), इसलिए योग \(5\sqrt{11}\) है। समान मूलों को जोड़ने से पहले सरल करें।
Login to save your score, XP, coins and progress. Login
