किस संख्या को अपरिमेय संख्या कहा जाता है?
Which number is called an irrational number?
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A जिसे (p / q) के रूप में लिखा जा सके / Can be written as (p / q)
B जिसे (p / q) के रूप में नहीं लिखा जा सके / Cannot be written as (p / q)
C जो केवल पूर्णांक हो / Only an integer
D जो केवल शून्य हो / Only zero
Explanation opens after your attempt
Correct Answer
B. जिसे (p / q) के रूप में नहीं लिखा जा सके / Cannot be written as (p / q)
Step 1
Concept
An irrational number cannot be written as (p/q). In exams also check its decimal form.
Step 2
Why this answer is correct
The correct answer is B. जिसे (p / q) के रूप में नहीं लिखा जा सके / Cannot be written as (p / q). An irrational number cannot be written as (p/q). In exams also check its decimal form.
Step 3
Exam Tip
अपरिमेय संख्या को (p/q) के रूप में नहीं लिखा जा सकता। परीक्षा में दशमलव रूप भी देखें।
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इनमें से कौन-सी संख्या अपरिमेय है?
Which of the following numbers is irrational?
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A (4)
B (0.5)
C \(\sqrt{2}\)
D (7 / 8)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{2}\)
Step 1
Concept
\(\sqrt{2}\) is an irrational number. A square root is easily rational only for perfect squares.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{2}\). \(\sqrt{2}\) is an irrational number. A square root is easily rational only for perfect squares.
Step 3
Exam Tip
\(\sqrt{2}\) अपरिमेय संख्या है। पूर्ण वर्ग का वर्गमूल ही आसानी से परिमेय होता है।
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\(\sqrt{16}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{16}\)?
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A अपरिमेय / Irrational
B परिमेय / Rational
C ऋणात्मक अपरिमेय / Negative irrational
D अनिर्धारित / Undefined
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Step 1
Concept
\(\sqrt{16}=4\) so it is rational. The square root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is B. परिमेय / Rational. \(\sqrt{16}=4\) so it is rational. The square root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{16}=4\) होता है इसलिए यह परिमेय है। पूर्ण वर्ग का वर्गमूल परिमेय होता है।
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\(\sqrt{7}\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(\sqrt{7}\)?
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A यह परिमेय है / It is rational
B यह अपरिमेय है / It is irrational
C यह पूर्णांक है / It is an integer
D यह प्राकृतिक संख्या है / It is a natural number
Explanation opens after your attempt
Correct Answer
B. यह अपरिमेय है / It is irrational
Step 1
Concept
(7) is not a perfect square so \(\sqrt{7}\) is irrational. In exams first identify perfect squares.
Step 2
Why this answer is correct
The correct answer is B. यह अपरिमेय है / It is irrational. (7) is not a perfect square so \(\sqrt{7}\) is irrational. In exams first identify perfect squares.
Step 3
Exam Tip
(7) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{7}\) अपरिमेय है। परीक्षा में पहले पूर्ण वर्ग पहचानें।
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संख्या \(\pi\) के बारे में सही विकल्प चुनिए।
Choose the correct option about the number \(\pi\).
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A यह परिमेय है / It is rational
B यह अपरिमेय है / It is irrational
C यह (22 / 7) के बराबर है / It is equal to (22 / 7)
D यह पूर्णांक है / It is an integer
Explanation opens after your attempt
Correct Answer
B. यह अपरिमेय है / It is irrational
Step 1
Concept
\(\pi\) is irrational and (22/7) is only a common approximation. Keep equality and approximation different.
Step 2
Why this answer is correct
The correct answer is B. यह अपरिमेय है / It is irrational. \(\pi\) is irrational and (22/7) is only a common approximation. Keep equality and approximation different.
Step 3
Exam Tip
\(\pi\) अपरिमेय है और (22/7) केवल उसका मानक निकट मान है। बराबरी और निकट मान में फर्क रखें।
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इनमें से किसका दशमलव प्रसार असांत और अनावर्ती है?
Which of these has a non-terminating and non-repeating decimal expansion?
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A (1 / 4)
B (0.75)
C \(\sqrt{3}\)
D (2.5)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{3}\) is irrational so its decimal is non-terminating and non-repeating. This is the main test for irrational numbers.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{3}\). \(\sqrt{3}\) is irrational so its decimal is non-terminating and non-repeating. This is the main test for irrational numbers.
Step 3
Exam Tip
\(\sqrt{3}\) अपरिमेय है इसलिए इसका दशमलव असांत और अनावर्ती है। यही अपरिमेय की मुख्य पहचान है।
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दशमलव \(0.333\ldots\) किस प्रकार की संख्या है?
What type of number is the decimal \(0.333\ldots\)?
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A अपरिमेय / Irrational
B परिमेय / Rational
C न प्राकृतिक न परिमेय / Neither natural nor rational
D केवल पूर्णांक / Only integer
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Step 1
Concept
\(0.333\ldots\) 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 B. परिमेय / Rational. \(0.333\ldots\) is repeating so it is rational. A repeating decimal can be converted into a fraction.
Step 3
Exam Tip
\(0.333\ldots\) आवर्ती दशमलव है इसलिए परिमेय है। आवर्ती दशमलव को भिन्न में बदला जा सकता है।
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यदि (r) परिमेय है और (x) अपरिमेय है तो (r+x) सामान्यतः क्या होगा जब (r=5) और \(x=\sqrt{2}\)?
If (r) is rational and (x) is irrational then what is (r+x) generally when (r=5) and \(x=\sqrt{2}\)?
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A परिमेय / Rational
B अपरिमेय / Irrational
C शून्य / Zero
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(5+\sqrt{2}\) is irrational because adding a rational and an irrational gives an irrational. In such questions watch the irrational part.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(5+\sqrt{2}\) is irrational because adding a rational and an irrational gives an irrational. In such questions watch the irrational part.
Step 3
Exam Tip
\(5+\sqrt{2}\) अपरिमेय है क्योंकि परिमेय में अपरिमेय जोड़ने से अपरिमेय मिलता है। ऐसे सवाल में अपरिमेय भाग देखें।
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\(\sqrt{5}\) का (3) गुना किस प्रकार की संख्या है?
What type of number is (3) times \(\sqrt{5}\)?
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D प्राकृतिक / Natural
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(3\sqrt{5}\) is irrational because multiplying by a non-zero rational keeps it irrational. Remember the multiplier must not be (0).
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(3\sqrt{5}\) is irrational because multiplying by a non-zero rational keeps it irrational. Remember the multiplier must not be (0).
Step 3
Exam Tip
\(3\sqrt{5}\) अपरिमेय है क्योंकि शून्येतर परिमेय से गुणा करने पर अपरिमेय ही रहता है। गुणक (0) न हो यह ध्यान रखें।
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\(0\times\sqrt{11}\) किसके बराबर है?
What is \(0\times\sqrt{11}\) equal to?
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A अपरिमेय संख्या / Irrational number
B (0)
C \(\sqrt{11}\)
D (11)
Explanation opens after your attempt
Step 1
Concept
\(0\times\sqrt{11}=0\) and (0) is rational. Multiplication by zero always gives zero.
Step 2
Why this answer is correct
The correct answer is B. (0). \(0\times\sqrt{11}=0\) and (0) is rational. Multiplication by zero always gives zero.
Step 3
Exam Tip
\(0\times\sqrt{11}=0\) होता है और (0) परिमेय है। शून्य से गुणा करने पर परिणाम हमेशा शून्य होता है।
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इनमें से कौन-सा वर्गमूल अपरिमेय है?
Which of these square roots is irrational?
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A \(\sqrt{9}\)
B \(\sqrt{25}\)
C \(\sqrt{10}\)
D \(\sqrt{36}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{10}\)
Step 1
Concept
(10) is not a perfect square so \(\sqrt{10}\) is irrational. Remembering perfect squares is useful.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{10}\). (10) is not a perfect square so \(\sqrt{10}\) is irrational. Remembering perfect squares is useful.
Step 3
Exam Tip
(10) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{10}\) अपरिमेय है। पूर्ण वर्गों की सूची याद रखना उपयोगी है।
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इनमें से कौन-सा वर्गमूल परिमेय है?
Which of these square roots is rational?
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A \(\sqrt{6}\)
B \(\sqrt{49}\)
C \(\sqrt{15}\)
D \(\sqrt{30}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{49}\)
Step 1
Concept
\(\sqrt{49}=7\) so it is rational. The square root of a perfect square is a rational integer.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{49}\). \(\sqrt{49}=7\) so it is rational. The square root of a perfect square is a rational integer.
Step 3
Exam Tip
\(\sqrt{49}=7\) इसलिए यह परिमेय है। पूर्ण वर्ग का वर्गमूल हमेशा परिमेय पूर्णांक होता है।
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(1) और (2) के बीच कौन-सी अपरिमेय संख्या है?
Which irrational number lies between (1) and (2)?
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A \(\sqrt{4}\)
B \(\sqrt{2}\)
C (3 / 2)
D (1.5)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{2}\)
Step 1
Concept
\(\sqrt{2}\) lies between (1) and (2) and is irrational. Estimate using nearby squares.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{2}\). \(\sqrt{2}\) lies between (1) and (2) and is irrational. Estimate using nearby squares.
Step 3
Exam Tip
\(\sqrt{2}\) का मान (1) और (2) के बीच होता है और यह अपरिमेय है। अंतराल में वर्गों से अनुमान लगाएं।
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दशमलव \(0.101001000100001\ldots\) किस प्रकार का है?
What type of decimal is \(0.101001000100001\ldots\)?
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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 is non-terminating and non-repeating so it is irrational. Understand the pattern before calling it repeating.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय / Irrational. This decimal is non-terminating and non-repeating so it is irrational. Understand the pattern before calling it repeating.
Step 3
Exam Tip
यह दशमलव असांत और अनावर्ती है इसलिए अपरिमेय है। केवल दोहराव दिखने से पहले पूरा पैटर्न समझें।
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दशमलव \(0.121212\ldots\) किस प्रकार की संख्या है?
What type of number is \(0.121212\ldots\)?
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A अपरिमेय / Irrational
B परिमेय / Rational
C ऋणात्मक पूर्णांक / Negative integer
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Step 1
Concept
(12) repeats again and again so it is a repeating decimal. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is B. परिमेय / Rational. (12) repeats again and again so it is a repeating decimal. A repeating decimal is rational.
Step 3
Exam Tip
(12) बार-बार दोहर रहा है इसलिए यह आवर्ती दशमलव है। आवर्ती दशमलव परिमेय होता है।
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\(-\sqrt{13}\) किस प्रकार की संख्या है?
What type of number is \(-\sqrt{13}\)?
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A परिमेय / Rational
B अपरिमेय / Irrational
C शून्य / Zero
D धनात्मक पूर्णांक / Positive integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{13}\) is irrational so its negative is also irrational. Changing the sign does not change the type.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(\sqrt{13}\) is irrational so its negative is also irrational. Changing the sign does not change the type.
Step 3
Exam Tip
\(\sqrt{13}\) अपरिमेय है इसलिए उसका ऋणात्मक भी अपरिमेय है। चिन्ह बदलने से प्रकार नहीं बदलता।
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(\(\sqrt{3}\)2 ) किसके बराबर है?
What is (\(\sqrt{3}\)2 ) equal to?
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A \(\sqrt{3}\)
B (3)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
(\(\sqrt{3}\)2 =3) which is rational. The square of an irrational can sometimes be rational.
Step 2
Why this answer is correct
The correct answer is B. (3). (\(\sqrt{3}\)2 =3) which is rational. The square of an irrational can sometimes be rational.
Step 3
Exam Tip
(\(\sqrt{3}\)2 =3) होता है जो परिमेय है। अपरिमेय का वर्ग कभी-कभी परिमेय हो सकता है।
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(\sqrt{2}+\(-\sqrt{2}\)) का मान क्या है?
What is the value of (\sqrt{2}+\(-\sqrt{2}\))?
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A \(\sqrt{2}\)
B \(2\sqrt{2}\)
C (0)
D (2)
Explanation opens after your attempt
Step 1
Concept
The two terms are opposites so the sum is (0). The sum of two irrationals can also be rational.
Step 2
Why this answer is correct
The correct answer is C. (0). The two terms are opposites so the sum is (0). The sum of two irrationals can also be rational.
Step 3
Exam Tip
दोनों पद एक-दूसरे के विपरीत हैं इसलिए योग (0) है। दो अपरिमेयों का योग परिमेय भी हो सकता है।
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\(\sqrt{2}\times\sqrt{2}\) का परिणाम क्या है?
What is the result of \(\sqrt{2}\times\sqrt{2}\)?
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A अपरिमेय \(\sqrt{2}\) / Irrational \(\sqrt{2}\)
B परिमेय (2) / Rational (2)
C परिमेय (4) / Rational (4)
D अपरिमेय \(2\sqrt{2}\) / Irrational \(2\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
B. परिमेय (2) / Rational (2)
Step 1
Concept
\(\sqrt{2}\times\sqrt{2}=2\). The product of two irrationals can be rational.
Step 2
Why this answer is correct
The correct answer is B. परिमेय (2) / Rational (2). \(\sqrt{2}\times\sqrt{2}=2\). The product of two irrationals can be rational.
Step 3
Exam Tip
\(\sqrt{2}\times\sqrt{2}=2\) होता है। दो अपरिमेयों का गुणनफल परिमेय हो सकता है।
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\(\sqrt{2}\times\sqrt{3}\) किसके बराबर है?
What is \(\sqrt{2}\times\sqrt{3}\) equal to?
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A \(\sqrt{5}\)
B \(\sqrt{6}\)
C (6)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{6}\)
Step 1
Concept
\(\sqrt{2}\times\sqrt{3}=\sqrt{6}\) and \(\sqrt{6}\) is irrational. In multiplication multiply the numbers inside roots.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{6}\). \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\) and \(\sqrt{6}\) is irrational. In multiplication multiply the numbers inside roots.
Step 3
Exam Tip
\(\sqrt{2}\times\sqrt{3}=\sqrt{6}\) होता है और \(\sqrt{6}\) अपरिमेय है। गुणन में अंदर की संख्याएँ गुणा करें।
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\(2+\sqrt{5}\) किस प्रकार की संख्या है?
What type of number is \(2+\sqrt{5}\)?
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D प्राकृतिक / Natural
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
Adding irrational \(\sqrt{5}\) to rational (2) gives an irrational number. Identify the irrational part separately.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. Adding irrational \(\sqrt{5}\) to rational (2) gives an irrational number. Identify the irrational part separately.
Step 3
Exam Tip
परिमेय (2) में अपरिमेय \(\sqrt{5}\) जोड़ने से अपरिमेय संख्या मिलती है। अपरिमेय भाग को अलग पहचानें।
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\(9-\sqrt{7}\) किस प्रकार की संख्या है?
What type of number is \(9-\sqrt{7}\)?
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A अपरिमेय / Irrational
B परिमेय / Rational
C शून्य / Zero
D पूर्ण वर्ग / Perfect square
Explanation opens after your attempt
Correct Answer
A. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{7}\) is irrational so \(9-\sqrt{7}\) is also irrational. Adding or subtracting a rational keeps irrationality.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय / Irrational. \(\sqrt{7}\) is irrational so \(9-\sqrt{7}\) is also irrational. Adding or subtracting a rational keeps irrationality.
Step 3
Exam Tip
\(\sqrt{7}\) अपरिमेय है इसलिए \(9-\sqrt{7}\) भी अपरिमेय है। परिमेय घटाने या जोड़ने से अपरिमेयता बनी रहती है।
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\(\sqrt{\frac{4}{9}}\) किसके बराबर है?
What is \(\sqrt{\frac{4}{9}}\) equal to?
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A \(\frac{2}{3}\)
B \(\frac{4}{9}\)
C \(\sqrt{4}\)
D \(\frac{3}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{2}{3}\)
Step 1
Concept
\(\sqrt{\frac{4}{9}}=\frac{2}{3}\) so it is rational. Take square roots of numerator and denominator.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{2}{3}\). \(\sqrt{\frac{4}{9}}=\frac{2}{3}\) so it is rational. Take square roots of numerator and denominator.
Step 3
Exam Tip
\(\sqrt{\frac{4}{9}}=\frac{2}{3}\) है इसलिए यह परिमेय है। भिन्न में अंश और हर दोनों का वर्गमूल लें।
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\(\sqrt{\frac{2}{9}}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{\frac{2}{9}}\)?
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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
\(\sqrt{\frac{2}{9}}=\frac{\sqrt{2}}{3}\) which is irrational. Be careful when the numerator is not a perfect square.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(\sqrt{\frac{2}{9}}=\frac{\sqrt{2}}{3}\) which is irrational. Be careful when the numerator is not a perfect square.
Step 3
Exam Tip
\(\sqrt{\frac{2}{9}}=\frac{\sqrt{2}}{3}\) है जो अपरिमेय है। यदि अंश पूर्ण वर्ग न हो तो ध्यान रखें।
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इनमें से कौन-सी संख्या अपरिमेय नहीं है?
Which of these numbers is not irrational?
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A \(\sqrt{11}\)
B \(\sqrt{17}\)
C \(\sqrt{25}\)
D \(\sqrt{19}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{25}\)
Step 1
Concept
\(\sqrt{25}=5\) so it is rational. Square roots of perfect squares are not irrational.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{25}\). \(\sqrt{25}=5\) so it is rational. Square roots of perfect squares are not irrational.
Step 3
Exam Tip
\(\sqrt{25}=5\) है इसलिए यह परिमेय है। पूर्ण वर्गों के वर्गमूल अपरिमेय नहीं होते।
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दशमलव \(0.123456789101112\ldots\) को किस प्रकार माना जाता है?
How is the decimal \(0.123456789101112\ldots\) considered?
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A सांत परिमेय / Terminating rational
B आवर्ती परिमेय / Repeating rational
C अपरिमेय / Irrational
D ऋणात्मक पूर्णांक / Negative integer
Explanation opens after your attempt
Correct Answer
C. अपरिमेय / Irrational
Step 1
Concept
This decimal is non-terminating and non-repeating so it is irrational. It has no fixed repeating block.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय / Irrational. This decimal is non-terminating and non-repeating so it is irrational. It has no fixed repeating block.
Step 3
Exam Tip
यह दशमलव असांत और अनावर्ती है इसलिए अपरिमेय है। दोहराने वाला निश्चित ब्लॉक नहीं है।
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किस संख्या को (p/q) रूप में लिखा जा सकता है जहाँ \(q\neq0\)?
Which number can be written in the form (p/q) where \(q\neq0\)?
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C केवल मूल संख्या / Only radical number
D केवल दशमलव संख्या / Only decimal number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The form (p/q) identifies a rational number. An irrational number cannot be written so.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The form (p/q) identifies a rational number. An irrational number cannot be written so.
Step 3
Exam Tip
(p/q) रूप परिमेय संख्या की पहचान है। अपरिमेय को ऐसे नहीं लिखा जा सकता।
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\(\sqrt{0}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{0}\)?
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A अपरिमेय / Irrational
B परिमेय / Rational
C ऋणात्मक / Negative
D अनिर्धारित / Undefined
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Step 1
Concept
\(\sqrt{0}=0\) and (0) is rational. Zero can be written as (0/1).
Step 2
Why this answer is correct
The correct answer is B. परिमेय / Rational. \(\sqrt{0}=0\) and (0) is rational. Zero can be written as (0/1).
Step 3
Exam Tip
\(\sqrt{0}=0\) और (0) परिमेय है। शून्य को भी (0/1) लिखा जा सकता है।
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\(\sqrt{1}\) का सही प्रकार चुनिए।
Choose the correct type of \(\sqrt{1}\).
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A परिमेय / Rational
B अपरिमेय / Irrational
C न परिमेय न अपरिमेय / Neither rational nor irrational
D अनंत / Infinite
Explanation opens after your attempt
Correct Answer
A. परिमेय / Rational
Step 1
Concept
\(\sqrt{1}=1\) so it is rational. (1) is a perfect square.
Step 2
Why this answer is correct
The correct answer is A. परिमेय / Rational. \(\sqrt{1}=1\) so it is rational. (1) is a perfect square.
Step 3
Exam Tip
\(\sqrt{1}=1\) है इसलिए यह परिमेय है। (1) पूर्ण वर्ग है।
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(3.14) किस प्रकार की संख्या है?
What type of number is (3.14)?
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A अपरिमेय / Irrational
B परिमेय / Rational
C न वास्तविक / Not real
D अनंत दशमलव / Infinite decimal
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Step 1
Concept
(3.14) is a terminating decimal so it is rational. A terminating decimal can be converted into a fraction.
Step 2
Why this answer is correct
The correct answer is B. परिमेय / Rational. (3.14) is a terminating decimal so it is rational. A terminating decimal can be converted into a fraction.
Step 3
Exam Tip
(3.14) सांत दशमलव है इसलिए परिमेय है। सांत दशमलव को भिन्न में बदला जा सकता है।
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\(\sqrt{18}\) को सरल करने पर क्या मिलता है?
What do we get after simplifying \(\sqrt{18}\)?
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A \(3\sqrt{2}\)
B \(9\sqrt{2}\)
C \(2\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\). Therefore \(\sqrt{18}\) is irrational.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}\). \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\). Therefore \(\sqrt{18}\) is irrational.
Step 3
Exam Tip
\(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\) होता है। इसलिए \(\sqrt{18}\) अपरिमेय है।
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\(\sqrt{50}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{50}\)?
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A \(10\sqrt{5}\)
B \(25\sqrt{2}\)
C \(5\sqrt{2}\)
D \(2\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
C. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\). Since \(\sqrt{2}\) remains, it is irrational.
Step 2
Why this answer is correct
The correct answer is C. \(5\sqrt{2}\). \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\). Since \(\sqrt{2}\) remains, it is irrational.
Step 3
Exam Tip
\(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\) है। \(\sqrt{2}\) बचने से यह अपरिमेय है।
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\(\sqrt{0.25}\) किसके बराबर है?
What is \(\sqrt{0.25}\) equal to?
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A (0.05)
B (0.5)
C (2.5)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{0.25}=0.5\) so it is rational. Recognize decimals as squares when possible.
Step 2
Why this answer is correct
The correct answer is B. (0.5). \(\sqrt{0.25}=0.5\) so it is rational. Recognize decimals as squares when possible.
Step 3
Exam Tip
\(\sqrt{0.25}=0.5\) है इसलिए यह परिमेय है। दशमलव को वर्ग रूप में पहचानें।
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\(|-\sqrt{5}|\) किसके बराबर है?
What is \(|-\sqrt{5}|\) equal to?
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A \(-\sqrt{5}\)
B \(\sqrt{5}\)
C (5)
D (0)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{5}\)
Step 1
Concept
Absolute value removes the negative sign so the value is \(\sqrt{5}\). \(\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{5}\). Absolute value removes the negative sign so the value is \(\sqrt{5}\). \(\sqrt{5}\) is irrational.
Step 3
Exam Tip
मापांक ऋणात्मक चिन्ह हटाता है इसलिए मान \(\sqrt{5}\) है। \(\sqrt{5}\) अपरिमेय है।
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\(\frac{\sqrt{12}}{\sqrt{3}}\) का मान क्या है?
What is the value of \(\frac{\sqrt{12}}{\sqrt{3}}\)?
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A (2)
B \(\sqrt{4}\)
C \(\sqrt{9}\)
D \(\sqrt{15}\)
Explanation opens after your attempt
Step 1
Concept
\(\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{4}=2\). The final value is rational.
Step 2
Why this answer is correct
The correct answer is A. (2). \(\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{4}=2\). The final value is rational.
Step 3
Exam Tip
\(\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{4}=2\) है। अंतिम मान परिमेय है।
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\(\frac{\sqrt{8}}{\sqrt{2}}\) का सरल मान कौन-सा है?
Which is the simplified value of \(\frac{\sqrt{8}}{\sqrt{2}}\)?
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A (2)
B \(\sqrt{6}\)
C (4)
D \(\sqrt{10}\)
Explanation opens after your attempt
Step 1
Concept
\(\frac{\sqrt{8}}{\sqrt{2}}=\sqrt{4}=2\). The type can change after simplification.
Step 2
Why this answer is correct
The correct answer is A. (2). \(\frac{\sqrt{8}}{\sqrt{2}}=\sqrt{4}=2\). The type can change after simplification.
Step 3
Exam Tip
\(\frac{\sqrt{8}}{\sqrt{2}}=\sqrt{4}=2\) होता है। सरलीकरण के बाद प्रकार बदल सकता है।
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\(1+\sqrt{2}\) किस प्रकार की संख्या है?
What type of number is \(1+\sqrt{2}\)?
#number-systems
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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
\(\sqrt{2}\) is irrational so \(1+\sqrt{2}\) is also irrational. Adding a rational number does not remove the irrational part.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(\sqrt{2}\) is irrational so \(1+\sqrt{2}\) is also irrational. Adding a rational number does not remove the irrational part.
Step 3
Exam Tip
\(\sqrt{2}\) अपरिमेय है इसलिए \(1+\sqrt{2}\) भी अपरिमेय है। परिमेय संख्या जोड़ने से अपरिमेय भाग खत्म नहीं होता।
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इनमें से कौन-सा उदाहरण असांत अनावर्ती दशमलव का है?
Which is an example of a non-terminating non-repeating decimal?
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A \(0.666\ldots\)
B (0.25)
C \(1.010010001\ldots\)
D \(2.777\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(1.010010001\ldots\)
Step 1
Concept
\(1.010010001\ldots\) has no fixed repetition. So it is an example of an irrational decimal.
Step 2
Why this answer is correct
The correct answer is C. \(1.010010001\ldots\). \(1.010010001\ldots\) has no fixed repetition. So it is an example of an irrational decimal.
Step 3
Exam Tip
\(1.010010001\ldots\) में निश्चित दोहराव नहीं है। इसलिए यह अपरिमेय दशमलव का उदाहरण है।
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\(\sqrt{20}\) को सरल करने पर कौन-सा रूप मिलता है?
Which form is obtained after simplifying \(\sqrt{20}\)?
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A \(2\sqrt{5}\)
B \(5\sqrt{2}\)
C \(4\sqrt{5}\)
D (10)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Because of \(\sqrt{5}\), it is irrational.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{5}\). \(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Because of \(\sqrt{5}\), it is irrational.
Step 3
Exam Tip
\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\) है। \(\sqrt{5}\) के कारण यह अपरिमेय है।
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\(\sqrt{64}\) और \(\sqrt{65}\) में कौन-सी संख्या अपरिमेय है?
Between \(\sqrt{64}\) and \(\sqrt{65}\), which number is irrational?
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A \(\sqrt{64}\)
B \(\sqrt{65}\)
C दोनों परिमेय / Both rational
D दोनों पूर्णांक / Both integers
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{65}\)
Step 1
Concept
\(\sqrt{64}=8\) is rational but (65) is not a perfect square. Therefore \(\sqrt{65}\) is irrational.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{65}\). \(\sqrt{64}=8\) is rational but (65) is not a perfect square. Therefore \(\sqrt{65}\) is irrational.
Step 3
Exam Tip
\(\sqrt{64}=8\) परिमेय है लेकिन (65) पूर्ण वर्ग नहीं है। इसलिए \(\sqrt{65}\) अपरिमेय है।
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कौन-सा विकल्प अपरिमेय संख्या का सही उदाहरण है?
Which option is a correct example of an irrational number?
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A (6 / 11)
B (0.875)
C (-3)
D \(\sqrt{23}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{23}\)
Step 1
Concept
(23) is not a perfect square so \(\sqrt{23}\) is irrational. Fractions and terminating decimals are rational.
Step 2
Why this answer is correct
The correct answer is D. \(\sqrt{23}\). (23) is not a perfect square so \(\sqrt{23}\) is irrational. Fractions and terminating decimals are rational.
Step 3
Exam Tip
(23) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{23}\) अपरिमेय है। भिन्न और सांत दशमलव परिमेय होते हैं।
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\(4\sqrt{3}\) में कौन-सा भाग अपरिमेयता का कारण है?
Which part causes irrationality in \(4\sqrt{3}\)?
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A (4)
B \(\sqrt{3}\)
C गुणन चिह्न / Multiplication sign
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{3}\) is irrational so \(4\sqrt{3}\) is irrational. A non-zero rational multiplier does not change the type.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{3}\). \(\sqrt{3}\) is irrational so \(4\sqrt{3}\) is irrational. A non-zero rational multiplier does not change the type.
Step 3
Exam Tip
\(\sqrt{3}\) अपरिमेय है इसलिए \(4\sqrt{3}\) अपरिमेय है। शून्येतर परिमेय गुणक प्रकार नहीं बदलता।
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\(\sqrt{81}+ \sqrt{2}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{81}+ \sqrt{2}\)?
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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
\(\sqrt{81}=9\) and \(9+\sqrt{2}\) is irrational. Simplify first then decide the type.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(\sqrt{81}=9\) and \(9+\sqrt{2}\) is irrational. Simplify first then decide the type.
Step 3
Exam Tip
\(\sqrt{81}=9\) है और \(9+\sqrt{2}\) अपरिमेय है। पहले सरल करें फिर संख्या का प्रकार तय करें।
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\(\sqrt{27}-\sqrt{12}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{27}-\sqrt{12}\)?
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#irrational-numbers
#easy
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A \(\sqrt{15}\)
B \(\sqrt{3}\)
C \(3\sqrt{3}\)
D \(5\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\) so the difference is \(\sqrt{3}\). The result is irrational.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{3}\). \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\) so the difference is \(\sqrt{3}\). The result is irrational.
Step 3
Exam Tip
\(\sqrt{27}=3\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) इसलिए अंतर \(\sqrt{3}\) है। परिणाम अपरिमेय है।
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कौन-सा कथन अपरिमेय संख्या के लिए सही है?
Which statement is true for an irrational number?
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A उसका दशमलव हमेशा सांत होता है / Its decimal is always terminating
B उसका दशमलव हमेशा आवर्ती होता है / Its decimal is always repeating
C उसे (p / q) रूप में लिखा जा सकता है / It can be written as (p / q)
D उसे (p / q) रूप में नहीं लिखा जा सकता / It cannot be written as (p / q)
Explanation opens after your attempt
Correct Answer
D. उसे (p / q) रूप में नहीं लिखा जा सकता / It cannot be written as (p / q)
Step 1
Concept
An irrational number cannot be written in the form (p/q). Remember this basic definition for exams.
Step 2
Why this answer is correct
The correct answer is D. उसे (p / q) रूप में नहीं लिखा जा सकता / It cannot be written as (p / q). An irrational number cannot be written in the form (p/q). Remember this basic definition for exams.
Step 3
Exam Tip
अपरिमेय संख्या को (p/q) रूप में नहीं लिखा जा सकता। परीक्षा में यही मूल परिभाषा याद रखें।
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\(\sqrt[3]{8}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt[3]{8}\)?
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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
\(\sqrt[3]{8}=2\) 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. \(\sqrt[3]{8}=2\) so it is rational. The cube root of a perfect cube is rational.
Step 3
Exam Tip
\(\sqrt[3]{8}=2\) है इसलिए यह परिमेय है। पूर्ण घन का घनमूल परिमेय होता है।
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\(\sqrt{2}+3\sqrt{2}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{2}+3\sqrt{2}\)?
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A \(4\sqrt{2}\)
B \(3\sqrt{4}\)
C \(5\sqrt{2}\)
D (4)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
Adding like radicals gives \(\sqrt{2}+3\sqrt{2}=4\sqrt{2}\). It is still irrational.
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{2}\). Adding like radicals gives \(\sqrt{2}+3\sqrt{2}=4\sqrt{2}\). It is still irrational.
Step 3
Exam Tip
समान मूलों को जोड़ने पर \(\sqrt{2}+3\sqrt{2}=4\sqrt{2}\) मिलता है। यह अभी भी अपरिमेय है।
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\(\sqrt{5}\) और \(\sqrt{20}\) का योग किसके बराबर है?
What is the sum of \(\sqrt{5}\) and \(\sqrt{20}\)?
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A \(2\sqrt{5}\)
B \(3\sqrt{5}\)
C \(\sqrt{25}\)
D \(5\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
B. \(3\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\) so the sum is \(3\sqrt{5}\). Simplify radicals first.
Step 2
Why this answer is correct
The correct answer is B. \(3\sqrt{5}\). \(\sqrt{20}=2\sqrt{5}\) so the sum is \(3\sqrt{5}\). Simplify radicals first.
Step 3
Exam Tip
\(\sqrt{20}=2\sqrt{5}\) इसलिए योग \(3\sqrt{5}\) है। पहले मूल को सरल करें।
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\(\sqrt{98}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{98}\)?
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A \(7\sqrt{2}\)
B \(2\sqrt{7}\)
C \(14\sqrt{2}\)
D \(49\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\). Since \(\sqrt{2}\) remains, it is irrational.
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{2}\). \(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\). Since \(\sqrt{2}\) remains, it is irrational.
Step 3
Exam Tip
\(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\) होता है। \(\sqrt{2}\) बचने से यह अपरिमेय है।
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\(2\sqrt{6}-\sqrt{6}\) का सरल रूप क्या है?
What is the simplified form of \(2\sqrt{6}-\sqrt{6}\)?
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A \(\sqrt{6}\)
B (2)
C (6)
D \(3\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{6}\)
Step 1
Concept
Subtracting like radicals gives \(2\sqrt{6}-\sqrt{6}=\sqrt{6}\). \(\sqrt{6}\) is an irrational number.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{6}\). Subtracting like radicals gives \(2\sqrt{6}-\sqrt{6}=\sqrt{6}\). \(\sqrt{6}\) is an irrational number.
Step 3
Exam Tip
समान मूलों को घटाने पर \(2\sqrt{6}-\sqrt{6}=\sqrt{6}\) मिलता है। \(\sqrt{6}\) अपरिमेय संख्या है।
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