यदि \(\sqrt{n}\) अपरिमेय है, तो (n) के लिए कौन-सा मान सही हो सकता है?
If \(\sqrt{n}\) is irrational, which value of (n) can be correct?
#real-numbers
#irrational-numbers
#square-root
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (36)
B (49)
C (52)
D (64)
Explanation opens after your attempt
Step 1
Concept
किसी पूर्ण वर्ग का वर्गमूल परिमेय होता है। / The square root of a perfect square is rational.
Step 2
Why this answer is correct
(52) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{52}\) अपरिमेय होगा। / (52) is not a perfect square, so \(\sqrt{52}\) is irrational.
Step 3
Exam Tip
ऐसे प्रश्नों में दिए गए मानों में पूर्ण वर्गों को पहले हटा दें। / In such questions, eliminate perfect squares first.
Login to save your score, XP, coins and progress. Login
निम्नलिखित में से कौन-सा परिणाम अपरिमेय है?
Which of the following results is irrational?
#real-numbers
#irrational-result
#concept
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{9}+\sqrt{16}\)
B \(\sqrt{7}\times\sqrt{28}\)
C \(\sqrt{11}+2\)
D \(\sqrt{25}-\sqrt{4}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{11}+2\)
Step 1
Concept
पहले हर विकल्प को सरल करें। / Simplify each option first.
Step 2
Why this answer is correct
\(\sqrt{11}\) अपरिमेय है और (2) परिमेय है, इसलिए \(\sqrt{11}+2\) अपरिमेय रहेगा। / \(\sqrt{11}\) is irrational and (2) is rational, so \(\sqrt{11}+2\) remains irrational.
Step 3
Exam Tip
परिमेय और अपरिमेय के योग को परिमेय न मानें। / Do not treat the sum of a rational and an irrational number as rational.
Login to save your score, XP, coins and progress. Login
\(\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-subtraction
#simplification
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(3\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{66}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\)। / \(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलें। / Convert radicals into like radicals before subtracting.
Login to save your score, XP, coins and progress. Login
यदि \(x=4+\sqrt{7}\), तो (x-4) कैसी संख्या है?
If \(x=4+\sqrt{7}\), what type of number is (x-4)?
#real-numbers
#irrational-expression
#sqrt7
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 प्राकृतिक / Natural
Explanation opens after your attempt
Correct Answer
C. अपरिमेय / Irrational
Step 1
Concept
(x-4=\(4+\sqrt{7}\)-4) होगा। / (x-4=\(4+\sqrt{7}\)-4).
Step 2
Why this answer is correct
इससे \(\sqrt{7}\) बचता है, जो अपरिमेय है। / This leaves \(\sqrt{7}\), which is irrational.
Step 3
Exam Tip
पहले अभिव्यक्ति को सरल करें, फिर संख्या की प्रकृति बताएं। / First simplify the expression, then identify the nature of the number.
Login to save your score, XP, coins and progress. Login
निम्नलिखित में से कौन-सी संख्या परिमेय नहीं है?
Which of the following numbers is not rational?
#real-numbers
#not-rational
#irrational
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (1.25)
B \(\frac{17}{4}\)
C \(\sqrt{45}\)
D \(0.8888\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{45}\)
Step 1
Concept
समाप्त दशमलव, भिन्न और आवर्ती दशमलव परिमेय होते हैं। / Terminating decimals, fractions, and recurring decimals are rational.
Step 2
Why this answer is correct
\(\sqrt{45}=3\sqrt{5}\), और \(\sqrt{5}\) अपरिमेय है। / \(\sqrt{45}=3\sqrt{5}\), and \(\sqrt{5}\) is irrational.
Step 3
Exam Tip
वर्गमूल को सरल करके उसकी प्रकृति पहचानें। / Simplify the square root to identify its nature.
Login to save your score, XP, coins and progress. Login
\(\sqrt{20}+\sqrt{45}+\sqrt{125}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{20}+\sqrt{45}+\sqrt{125}\)?
#real-numbers
#radical-addition
#simplification
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(10\sqrt{5}\)
B \(12\sqrt{5}\)
C \(8\sqrt{5}\)
D \(15\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), और \(\sqrt{125}=5\sqrt{5}\)। / \(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), and \(\sqrt{125}=5\sqrt{5}\).
Step 2
Why this answer is correct
योग \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\) है। / The sum is \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals are like terms, add only the coefficients.
Login to save your score, XP, coins and progress. Login
कौन-सा कथन सही है?
Which statement is correct?
#real-numbers
#irrational-rules
#true-statement
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A दो अपरिमेय संख्याओं का योग हमेशा परिमेय होता है / The sum of two irrational numbers is always rational
B दो अपरिमेय संख्याओं का गुणनफल हमेशा परिमेय होता है / The product of two irrational numbers is always rational
C अशून्य परिमेय संख्या और अपरिमेय संख्या का गुणनफल अपरिमेय होता है / The product of a non-zero rational number and an irrational number is irrational
D हर अपरिमेय संख्या पूर्ण वर्ग होती है / Every irrational number is a perfect square
Explanation opens after your attempt
Correct Answer
C. अशून्य परिमेय संख्या और अपरिमेय संख्या का गुणनफल अपरिमेय होता है / The product of a non-zero rational number and an irrational number is irrational
Step 1
Concept
अशून्य परिमेय गुणक अपरिमेयता को खत्म नहीं करता। / A non-zero rational multiplier does not remove irrationality.
Step 2
Why this answer is correct
जैसे \(5\sqrt{2}\) अपरिमेय रहता है। / For example, \(5\sqrt{2}\) remains irrational.
Step 3
Exam Tip
हमेशा वाले कथनों को उदाहरण से जांचना अच्छी आदत है। / Testing always-type statements with examples is a good habit.
Login to save your score, XP, coins and progress. Login
\(\frac{7}{\sqrt{7}}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{7}{\sqrt{7}}\)?
#real-numbers
#rationalisation
#simplification
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{7}\)
B \(7\sqrt{7}\)
C \(\frac{1}{\sqrt{7}}\)
D (49)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{7}\)
Step 1
Concept
हर से वर्गमूल हटाने के लिए ऊपर और नीचे \(\sqrt{7}\) से गुणा करें। / Multiply numerator and denominator by \(\sqrt{7}\) to remove the root from the denominator.
Step 2
Why this answer is correct
\(\frac{7}{\sqrt{7}}=\frac{7\sqrt{7}}{7}=\sqrt{7}\)। / \(\frac{7}{\sqrt{7}}=\frac{7\sqrt{7}}{7}=\sqrt{7}\).
Step 3
Exam Tip
हर में वर्गमूल हो तो परिमेयकरण मदद करता है। / Rationalisation helps when the denominator contains a square root.
Login to save your score, XP, coins and progress. Login
यदि \(\sqrt{b}\) अपरिमेय है, तो कौन-सा परिणाम अवश्य परिमेय होगा?
If \(\sqrt{b}\) is irrational, which result will necessarily be rational?
#real-numbers
#irrational-square
#rational-result
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{b}+2\)
B (\(\sqrt{b}\)2 )
C \(3\sqrt{b}\)
D \(\sqrt{b}-1\)
Explanation opens after your attempt
Correct Answer
B. (\(\sqrt{b}\)2 )
Step 1
Concept
वर्गमूल का वर्ग करने पर अंदर की संख्या मिलती है। / Squaring a square root gives the number inside.
Step 2
Why this answer is correct
(\(\sqrt{b}\)2 =b), और (b) पूर्णांक हो तो परिमेय होता है। / (\(\sqrt{b}\)2 =b), and if (b) is an integer, it is rational.
Step 3
Exam Tip
अपरिमेय वर्गमूल का वर्ग परिमेय परिणाम दे सकता है। / The square of an irrational square root can give a rational result.
Login to save your score, XP, coins and progress. Login
कौन-सी संख्या (9) और (10) के बीच स्थित अपरिमेय संख्या है?
Which number is an irrational number between (9) and (10)?
#real-numbers
#irrational-between-numbers
#comparison
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{85}\)
B \(\sqrt{81}\)
C \(\sqrt{100}\)
D (9.5)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{85}\)
Step 1
Concept
(81<85<100), इसलिए \(9<\sqrt{85}<10\)। / Since (81<85<100), \(9<\sqrt{85}<10\).
Step 2
Why this answer is correct
(85) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{85}\) अपरिमेय है। / (85) is not a perfect square, so \(\sqrt{85}\) is irrational.
Step 3
Exam Tip
अंतराल वाले प्रश्न में पास के पूर्ण वर्गों का उपयोग करें। / In interval questions, use nearby perfect squares.
Login to save your score, XP, coins and progress. Login
\(\sqrt{75}+\sqrt{300}-\sqrt{48}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{75}+\sqrt{300}-\sqrt{48}\)?
#real-numbers
#radical-expression
#simplification
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(9\sqrt{3}\)
B \(11\sqrt{3}\)
C \(7\sqrt{3}\)
D \(\sqrt{327}\)
Explanation opens after your attempt
Correct Answer
B. \(11\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), और \(\sqrt{48}=4\sqrt{3}\)। / \(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), and \(\sqrt{48}=4\sqrt{3}\).
Step 2
Why this answer is correct
\(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\)। / \(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\).
Step 3
Exam Tip
जोड़ और घटाव से पहले सभी वर्गमूलों को सरल करें। / Simplify all radicals before addition and subtraction.
Login to save your score, XP, coins and progress. Login
दशमलव \(2.303003000300003\ldots\) में शून्यों की संख्या क्रमशः बढ़ रही है। यह संख्या कैसी है?
In the decimal \(2.303003000300003\ldots\), the number of zeros is increasing successively. What type of number is it?
#real-numbers
#decimal-expansion
#irrational
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A समाप्त दशमलव / Terminating decimal
B आवर्ती परिमेय / Recurring rational
C अपरिमेय / Irrational
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
C. अपरिमेय / Irrational
Step 1
Concept
इस दशमलव में कोई निश्चित समूह बार-बार नहीं दोहरता। / This decimal has no fixed block repeating again and again.
Step 2
Why this answer is correct
यह अनवसानी और अनावर्ती है, इसलिए अपरिमेय है। / It is non-terminating and non-recurring, so it is irrational.
Step 3
Exam Tip
दशमलव में दोहराव का निश्चित नियम देखकर ही निर्णय लें। / Decide by checking whether there is a fixed repeating pattern.
Login to save your score, XP, coins and progress. Login
कौन-सा युग्म दो अपरिमेय संख्याओं का है जिनका योग परिमेय है?
Which pair has two irrational numbers whose sum is rational?
#real-numbers
#irrational-sum
#rational-result
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{5},-\sqrt{5}\)
B \(\sqrt{2},\sqrt{8}\)
C \(\sqrt{3},\sqrt{12}\)
D \(\sqrt{6},2\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5},-\sqrt{5}\)
Step 1
Concept
\(\sqrt{5}\) और \(-\sqrt{5}\) दोनों अपरिमेय हैं। / \(\sqrt{5}\) and \(-\sqrt{5}\) are both irrational.
Step 2
Why this answer is correct
उनका योग (0) है, जो परिमेय है। / Their sum is (0), which is rational.
Step 3
Exam Tip
विपरीत अपरिमेय पदों का योग परिमेय हो सकता है। / Opposite irrational terms can give a rational sum.
Login to save your score, XP, coins and progress. Login
(\sqrt{5}\(3+\sqrt{5}\)) का मान क्या है?
What is the value of (\sqrt{5}\(3+\sqrt{5}\))?
#real-numbers
#radical-multiplication
#expression
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(3\sqrt{5}+5\)
B \(8\sqrt{5}\)
C \(3+5\sqrt{5}\)
D (15)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{5}+5\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\)। / Apply distribution: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\).
Step 2
Why this answer is correct
यह \(3\sqrt{5}+5\) बनता है। / This becomes \(3\sqrt{5}+5\).
Step 3
Exam Tip
समान वर्गमूलों के गुणन में \(\sqrt{5}\times\sqrt{5}=5\) याद रखें। / In such multiplication, remember \(\sqrt{5}\times\sqrt{5}=5\).
Login to save your score, XP, coins and progress. Login
कौन-सी संख्या \(4\sqrt{3}\) के बराबर है?
Which number is equal to \(4\sqrt{3}\)?
#real-numbers
#equivalent-radicals
#conversion
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{48}\)
B \(\sqrt{12}\)
C \(\sqrt{24}\)
D \(\sqrt{64}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{48}\)
Step 1
Concept
\(4\sqrt{3}=\sqrt{16}\sqrt{3}\)। / \(4\sqrt{3}=\sqrt{16}\sqrt{3}\).
Step 2
Why this answer is correct
यह \(\sqrt{48}\) के बराबर है। / This equals \(\sqrt{48}\).
Step 3
Exam Tip
बाहर के गुणांक को अंदर ले जाते समय उसका वर्ग गुणा करें। / When moving an outside coefficient inside the root, multiply by its square.
Login to save your score, XP, coins and progress. Login
(\left\(3+\sqrt{5}\right\)\left\(3-\sqrt{5}\right\)) का मान क्या है?
What is the value of (\left\(3+\sqrt{5}\right\)\left\(3-\sqrt{5}\right\))?
#real-numbers
#conjugates
#rational-result
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (4)
B (14)
C \(9+\sqrt{5}\)
D \(9-\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
यह ((a+b)(a-b)=a-2 -b-2 ) का रूप है। / This is of the form ((a+b)(a-b)=a-2 -b-2 ).
Step 2
Why this answer is correct
(32 -\(\sqrt{5}\)2 =9-5=4)। / (32 -\(\sqrt{5}\)2 =9-5=4).
Step 3
Exam Tip
संयुग्म गुणन में वर्गों का अंतर सीधे लगाएं। / In conjugate multiplication, directly use difference of squares.
Login to save your score, XP, coins and progress. Login
कौन-सा विकल्प अपरिमेय संख्या नहीं है?
Which option is not an irrational number?
#real-numbers
#not-irrational
#perfect-square
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{17}+1\)
B \(2\sqrt{13}\)
C \(\sqrt{196}-5\)
D \(7+\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{196}-5\)
Step 1
Concept
\(\sqrt{196}=14\) है। / \(\sqrt{196}=14\).
Step 2
Why this answer is correct
\(\sqrt{196}-5=9\), जो परिमेय संख्या है। / \(\sqrt{196}-5=9\), which is rational.
Step 3
Exam Tip
अपरिमेय नहीं पूछे जाने पर पूर्ण वर्ग वाले विकल्प ध्यान से देखें। / When asked for not irrational, carefully check perfect-square options.
Login to save your score, XP, coins and progress. Login
यदि \(a=\sqrt{3}+2\) और \(b=\sqrt{3}-2\), तो (ab) का मान क्या है?
If \(a=\sqrt{3}+2\) and \(b=\sqrt{3}-2\), what is the value of (ab)?
#real-numbers
#conjugate-product
#rational-result
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (1)
B (-1)
C (5)
D \(4\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
(ab=\(\sqrt{3}+2\)\(\sqrt{3}-2\)) है। / (ab=\(\sqrt{3}+2\)\(\sqrt{3}-2\)).
Step 2
Why this answer is correct
वर्गों के अंतर से (\(\sqrt{3}\)2 -22 =3-4=-1)। / Using difference of squares, (\(\sqrt{3}\)2 -22 =3-4=-1).
Step 3
Exam Tip
संयुग्म रूप पहचानकर गणना छोटी हो जाती है। / Recognising conjugate form makes the calculation shorter.
Login to save your score, XP, coins and progress. Login
\(\frac{1}{3+\sqrt{8}}\) का परिमेय हर वाला रूप क्या है?
What is the form of \(\frac{1}{3+\sqrt{8}}\) with a rational denominator?
#real-numbers
#rationalisation
#conjugate
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(3-\sqrt{8}\)
B \(3+\sqrt{8}\)
C \(\frac{3-\sqrt{8}}{17}\)
D \(\sqrt{8}-3\)
Explanation opens after your attempt
Correct Answer
A. \(3-\sqrt{8}\)
Step 1
Concept
हर \(3+\sqrt{8}\) का संयुग्म \(3-\sqrt{8}\) है। / The conjugate of \(3+\sqrt{8}\) is \(3-\sqrt{8}\).
Step 2
Why this answer is correct
\(\frac{1}{3+\sqrt{8}}\times\frac{3-\sqrt{8}}{3-\sqrt{8}}=\frac{3-\sqrt{8}}{9-8}=3-\sqrt{8}\)। / \(\frac{1}{3+\sqrt{8}}\times\frac{3-\sqrt{8}}{3-\sqrt{8}}=\frac{3-\sqrt{8}}{9-8}=3-\sqrt{8}\).
Step 3
Exam Tip
परिमेयकरण में हर का संयुग्म प्रयोग करें। / Use the conjugate of the denominator for rationalisation.
Login to save your score, XP, coins and progress. Login
कौन-सा कथन गलत है?
Which statement is false?
#real-numbers
#false-statement
#irrational-product
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{13}\) अपरिमेय है / \(\sqrt{13}\) is irrational
B \(\sqrt{81}\) परिमेय है / \(\sqrt{81}\) is rational
C दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय होता है / The product of two irrational numbers is always irrational
D \(0.565656\ldots\) परिमेय है / \(0.565656\ldots\) is rational
Explanation opens after your attempt
Correct Answer
C. दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय होता है / The product of two irrational numbers is always irrational
Step 1
Concept
\(\sqrt{2}\) और \(\sqrt{2}\) दोनों अपरिमेय हैं। / \(\sqrt{2}\) and \(\sqrt{2}\) are both irrational.
Step 2
Why this answer is correct
इनका गुणनफल (2) है, जो परिमेय है। / Their product is (2), which is rational.
Step 3
Exam Tip
हमेशा वाले कथन को प्रतिउदाहरण से जांचें। / Test always-type statements with a counterexample.
Login to save your score, XP, coins and progress. Login
\(\sqrt{18}+\sqrt{72}+\sqrt{162}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{18}+\sqrt{72}+\sqrt{162}\)?
#real-numbers
#radical-addition
#sqrt2
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(18\sqrt{2}\)
B \(12\sqrt{2}\)
C \(15\sqrt{2}\)
D \(9\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(18\sqrt{2}\)
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), और \(\sqrt{162}=9\sqrt{2}\)। / \(\sqrt{18}=3\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{162}=9\sqrt{2}\).
Step 2
Why this answer is correct
योग \(3\sqrt{2}+6\sqrt{2}+9\sqrt{2}=18\sqrt{2}\)। / The sum is \(3\sqrt{2}+6\sqrt{2}+9\sqrt{2}=18\sqrt{2}\).
Step 3
Exam Tip
कई वर्गमूलों को पहले पूरी तरह सरल करें। / Simplify all radicals completely first.
Login to save your score, XP, coins and progress. Login
यदि \(x=\sqrt{5}\), तो \(x^2+3x\) किसके बराबर है?
If \(x=\sqrt{5}\), what is \(x^2+3x\) equal to?
#real-numbers
#algebraic-expression
#irrational
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(5+3\sqrt{5}\)
B \(8\sqrt{5}\)
C (15)
D \(5+\sqrt{15}\)
Explanation opens after your attempt
Correct Answer
A. \(5+3\sqrt{5}\)
Step 1
Concept
(x-2 =\(\sqrt{5}\)2 =5)। / (x-2 =\(\sqrt{5}\)2 =5).
Step 2
Why this answer is correct
\(3x=3\sqrt{5}\), इसलिए \(x^2+3x=5+3\sqrt{5}\)। / \(3x=3\sqrt{5}\), so \(x^2+3x=5+3\sqrt{5}\).
Step 3
Exam Tip
वर्ग और गुणा को अलग-अलग सरल करें। / Simplify the square and the multiplication separately.
Login to save your score, XP, coins and progress. Login
यदि \(\sqrt{n}\) (10) और (11) के बीच है, तो (n) के लिए कौन-सा मान सही हो सकता है और \(\sqrt{n}\) अपरिमेय होगा?
If \(\sqrt{n}\) lies between (10) and (11), which value of (n) can be correct and makes \(\sqrt{n}\) irrational?
#real-numbers
#comparison
#irrational-numbers
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (100)
B (105)
C (121)
D (144)
Explanation opens after your attempt
Step 1
Concept
\(10<\sqrt{n}<11\) का अर्थ है (100<n<121)।
Step 2
Why this answer is correct
(105) इस अंतराल में है और पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{105}\) अपरिमेय है। / (105) lies in this interval and is not a perfect square, so \(\sqrt{105}\) is irrational.
Step 3
Exam Tip
वर्गमूल की सीमा के लिए दोनों तरफ वर्ग करें। / Square both bounds to handle square-root ranges.
Login to save your score, XP, coins and progress. Login
निम्नलिखित में से कौन-सा दशमलव परिमेय है?
Which of the following decimals is rational?
#real-numbers
#recurring-decimal
#rational
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(0.1010010001\ldots\)
B \(1.7320508\ldots\) बिना निश्चित दोहराव / \(1.7320508\ldots\) without fixed repetition
C \(0.272727\ldots\)
D \(2.010010001\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(0.272727\ldots\)
Step 1
Concept
आवर्ती दशमलव परिमेय होता है। / A recurring decimal is rational.
Step 2
Why this answer is correct
\(0.272727\ldots\) में (27) बार-बार दोहरता है। / In \(0.272727\ldots\), the block (27) repeats.
Step 3
Exam Tip
दशमलव में दोहरने वाला समूह पहचानना जरूरी है। / Identifying the repeating block in a decimal is important.
Login to save your score, XP, coins and progress. Login
(\left\(\sqrt{7}+1\right\)2 ) का मान क्या है?
What is the value of (\left\(\sqrt{7}+1\right\)2 )?
#real-numbers
#irrational-expression
#algebra
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(8+2\sqrt{7}\)
B \(7+\sqrt{7}\)
C \(8+\sqrt{7}\)
D \(9+2\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(8+2\sqrt{7}\)
Step 1
Concept
((a+b)2 =a-2 +2ab+b-2 ) लगाएं। / Use ((a+b)2 =a-2 +2ab+b-2 ).
Step 2
Why this answer is correct
(\(\sqrt{7}\)2 +2\sqrt{7}\times1+12 =7+2\sqrt{7}+1=8+2\sqrt{7})। / (\(\sqrt{7}\)2 +2\sqrt{7}\times1+12 =7+2\sqrt{7}+1=8+2\sqrt{7}).
Step 3
Exam Tip
मध्य पद (2ab) को भूलना सामान्य गलती है। / Forgetting the middle term (2ab) is a common mistake.
Login to save your score, XP, coins and progress. Login
यदि \(\sqrt{t}\) (6) और (7) के बीच है, तो (t) का कौन-सा मान संभव है?
If \(\sqrt{t}\) lies between (6) and (7), which value of (t) is possible?
#real-numbers
#square-root-interval
#comparison
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (35)
B (42)
C (49)
D (64)
Explanation opens after your attempt
Step 1
Concept
\(6<\sqrt{t}<7\) का अर्थ है (36<t<49)।
Step 2
Why this answer is correct
(42) इस अंतराल में है, इसलिए \(\sqrt{42}\) (6) और (7) के बीच होगा। / (42) lies in this interval, so \(\sqrt{42}\) lies between (6) and (7).
Step 3
Exam Tip
वर्गमूल के अंतराल को समझने के लिए सीमा संख्याओं का वर्ग करें। / Square the boundary numbers to understand square-root intervals.
Login to save your score, XP, coins and progress. Login
\(\frac{4}{\sqrt{2}}\) का परिमेय हर वाला सरल रूप क्या है?
What is the simplified form of \(\frac{4}{\sqrt{2}}\) with a rational denominator?
#real-numbers
#rationalisation
#sqrt2
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2\sqrt{2}\)
B \(\frac{4\sqrt{2}}{2}\)
C \(\sqrt{2}\)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{2}\)
Step 1
Concept
ऊपर और नीचे \(\sqrt{2}\) से गुणा करें। / Multiply numerator and denominator by \(\sqrt{2}\).
Step 2
Why this answer is correct
\(\frac{4}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}\)। / \(\frac{4}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}\).
Step 3
Exam Tip
परिमेयकरण के बाद उत्तर को पूरी तरह सरल करें। / After rationalising, simplify the answer completely.
Login to save your score, XP, coins and progress. Login
कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{8}\times\sqrt{18}\)
B \(\sqrt{12}\times\sqrt{27}\)
C \(\sqrt{15}\times\sqrt{60}\)
D \(\sqrt{2}\times\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{2}\times\sqrt{11}\)
Step 1
Concept
पहले गुणनफल में अंदर की संख्याएँ गुणा करें। / First multiply the numbers inside the roots.
Step 2
Why this answer is correct
पहले तीन में (144), (324), और (900) मिलते हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{22}\) है। / The first three give (144), (324), and (900), which are perfect squares; the fourth gives \(\sqrt{22}\).
Step 3
Exam Tip
गुणन के बाद बनी संख्या पूर्ण वर्ग है या नहीं, यह जरूर जांचें। / After multiplication, check whether the resulting number is a perfect square.
Login to save your score, XP, coins and progress. Login
\(\sqrt{128}+\sqrt{72}-\sqrt{50}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{128}+\sqrt{72}-\sqrt{50}\)?
#real-numbers
#radical-expression
#simplification
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(9\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{150}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), और \(\sqrt{50}=5\sqrt{2}\)। / \(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\).
Step 2
Why this answer is correct
\(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\)। / \(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
सभी वर्गमूलों को समान रूप में बदलकर ही जोड़-घटाव करें। / Convert all radicals into like form before adding or subtracting.
Login to save your score, XP, coins and progress. Login
यदि (p) परिमेय है और (q) अपरिमेय है, तो (p-q) कैसी संख्या होगी?
If (p) is rational and (q) is irrational, what type of number is (p-q)?
#real-numbers
#rational-irrational-difference
#conceptual
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A हमेशा परिमेय / Always rational
B हमेशा अपरिमेय / Always irrational
C हमेशा शून्य / Always zero
D हमेशा पूर्णांक / Always integer
Explanation opens after your attempt
Correct Answer
B. हमेशा अपरिमेय / Always irrational
Step 1
Concept
परिमेय संख्या में से अपरिमेय संख्या घटाने पर अपरिमेय भाग बचता है। / Subtracting an irrational number from a rational number leaves an irrational part.
Step 2
Why this answer is correct
यदि परिणाम परिमेय हो, तो (q=p-(p-q)) परिमेय हो जाएगा, जो गलत है। / If the result were rational, then (q=p-(p-q)) would be rational, which is impossible.
Step 3
Exam Tip
परिमेय और अपरिमेय के जोड़-घटाव के नियम याद रखें। / Remember the rules for addition and subtraction of rational and irrational numbers.
Login to save your score, XP, coins and progress. Login
\(\sqrt{c}\times\sqrt{12}=18\) और (c) धनात्मक है। (c) का मान क्या है?
If \(\sqrt{c}\times\sqrt{12}=18\) and (c) is positive, what is the value of (c)?
#real-numbers
#radical-equation
#square-root
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (18)
B (24)
C (27)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{c}\times\sqrt{12}=\sqrt{12c}\)। / \(\sqrt{c}\times\sqrt{12}=\sqrt{12c}\).
Step 2
Why this answer is correct
\(\sqrt{12c}=18\), इसलिए (12c=324) और (c=27)। / \(\sqrt{12c}=18\), so (12c=324) and (c=27).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करके हल करें। / In square-root equations, square both sides to solve.
Login to save your score, XP, coins and progress. Login
निम्नलिखित में से कौन-सा मान \(\sqrt{13}\) के सबसे निकट है?
Which of the following values is closest to \(\sqrt{13}\)?
#real-numbers
#approximation
#sqrt13
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3.21)
B (3.61)
C (3.91)
D (4.21)
Explanation opens after your attempt
Step 1
Concept
(9<13<16), इसलिए \(\sqrt{13}\) (3) और (4) के बीच है। / Since (9<13<16), \(\sqrt{13}\) lies between (3) and (4).
Step 2
Why this answer is correct
\(\sqrt{13}\approx3.606\), इसलिए (3.61) सबसे निकट है। / \(\sqrt{13}\approx3.606\), so (3.61) is the closest.
Step 3
Exam Tip
अनुमान में पहले पूर्ण वर्गों से सीमा तय करें। / In approximation, first set the range using perfect squares.
Login to save your score, XP, coins and progress. Login
कौन-सा विकल्प दो अपरिमेय संख्याओं का ऐसा अंतर दिखाता है जो परिमेय है?
Which option shows a difference of two irrational numbers that is rational?
#real-numbers
#irrational-difference
#rational-result
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{7}-\sqrt{7}\)
B \(\sqrt{8}-\sqrt{3}\)
C \(\sqrt{10}-2\)
D \(\sqrt{15}-\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{7}-\sqrt{7}\)
Step 1
Concept
\(\sqrt{7}\) और \(\sqrt{7}\) दोनों अपरिमेय हैं। / \(\sqrt{7}\) and \(\sqrt{7}\) are both irrational.
Step 2
Why this answer is correct
उनका अंतर (0) है, जो परिमेय है। / Their difference is (0), which is rational.
Step 3
Exam Tip
समान अपरिमेय पदों का अंतर परिमेय हो सकता है। / The difference of equal irrational terms can be rational.
Login to save your score, XP, coins and progress. Login
\(\sqrt{48}\times\sqrt{75}\) का मान क्या है?
What is the value of \(\sqrt{48}\times\sqrt{75}\)?
#real-numbers
#radical-product
#rational-result
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(30\sqrt{4}\)
B (60)
C (120)
D \(\sqrt{123}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{48}\times\sqrt{75}=\sqrt{3600}\)। / \(\sqrt{48}\times\sqrt{75}=\sqrt{3600}\).
Step 2
Why this answer is correct
\(\sqrt{3600}=60\), इसलिए परिणाम परिमेय है। / \(\sqrt{3600}=60\), so the result is rational.
Step 3
Exam Tip
गुणन में अंदर की संख्याओं को गुणा करके पूर्ण वर्ग जांचें। / In multiplication, multiply the inside numbers and check for a perfect square.
Login to save your score, XP, coins and progress. Login
यदि \(x=3-\sqrt{8}\), तो \(\frac{1}{x}\) क्या होगा?
If \(x=3-\sqrt{8}\), what is \(\frac{1}{x}\)?
#real-numbers
#rationalisation
#conjugate
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(3+\sqrt{8}\)
B \(3-\sqrt{8}\)
C \(\frac{3+\sqrt{8}}{17}\)
D \(\sqrt{8}-3\)
Explanation opens after your attempt
Correct Answer
A. \(3+\sqrt{8}\)
Step 1
Concept
\(\frac{1}{3-\sqrt{8}}\) में हर का संयुग्म \(3+\sqrt{8}\) है। / In \(\frac{1}{3-\sqrt{8}}\), the conjugate of the denominator is \(3+\sqrt{8}\).
Step 2
Why this answer is correct
हर (9-8=1) बनता है, इसलिए मान \(3+\sqrt{8}\) है। / The denominator becomes (9-8=1), so the value is \(3+\sqrt{8}\).
Step 3
Exam Tip
संयुग्म से परिमेयकरण करने पर हर जल्दी सरल होता है। / Rationalising with the conjugate quickly simplifies the denominator.
Login to save your score, XP, coins and progress. Login
यदि \(z=6+\sqrt{5}\), तो (z) की प्रकृति क्या है?
If \(z=6+\sqrt{5}\), what is the nature of (z)?
#real-numbers
#irrational-sum
#concept
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 सम संख्या / Even number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
(6) परिमेय है और \(\sqrt{5}\) अपरिमेय है। / (6) is rational and \(\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
परिमेय और अपरिमेय संख्या का योग अपरिमेय होता है। / The sum of a rational and an irrational number is irrational.
Step 3
Exam Tip
पूर्णांक जोड़ने से वर्गमूल वाला अपरिमेय भाग खत्म नहीं होता। / Adding an integer does not remove the irrational square-root part.
Login to save your score, XP, coins and progress. Login
\(\sqrt{363}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{363}-\sqrt{75}\)?
#real-numbers
#radical-subtraction
#sqrt3
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(6\sqrt{3}\)
B \(4\sqrt{3}\)
C \(8\sqrt{3}\)
D \(\sqrt{288}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{363}=11\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{363}=11\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
\(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\)। / \(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\).
Step 3
Exam Tip
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
Login to save your score, XP, coins and progress. Login
किस विकल्प में दी गई संख्या अपरिमेय है और (5) से छोटी है?
In which option is the given number irrational and less than (5)?
#real-numbers
#irrational-less-than
#comparison
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{30}\)
B \(\sqrt{24}\)
C \(\sqrt{25}\)
D (4.9)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{24}\)
Step 1
Concept
\(\sqrt{24}\) अपरिमेय है क्योंकि (24) पूर्ण वर्ग नहीं है। / \(\sqrt{24}\) is irrational because (24) is not a perfect square.
Step 2
Why this answer is correct
(16<24<25), इसलिए \(4<\sqrt{24}<5\)। / Since (16<24<25), \(4<\sqrt{24}<5\).
Step 3
Exam Tip
शर्तों वाले प्रश्न में अपरिमेयता और सीमा दोनों जांचें। / In condition-based questions, check both irrationality and range.
Login to save your score, XP, coins and progress. Login
(\left\(\sqrt{11}-\sqrt{2}\right\)\left\(\sqrt{11}+\sqrt{2}\right\)) का मान क्या है?
What is the value of (\left\(\sqrt{11}-\sqrt{2}\right\)\left\(\sqrt{11}+\sqrt{2}\right\))?
#real-numbers
#conjugate-product
#rational-result
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (9)
B (13)
C \(\sqrt{22}\)
D \(11+\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
यह ((a-b)(a+b)=a-2 -b-2 ) का रूप है। / This is of the form ((a-b)(a+b)=a-2 -b-2 ).
Step 2
Why this answer is correct
(\(\sqrt{11}\)2 -\(\sqrt{2}\)2 =11-2=9)। / (\(\sqrt{11}\)2 -\(\sqrt{2}\)2 =11-2=9).
Step 3
Exam Tip
संयुग्म गुणन में वर्गों का अंतर सीधे लगाएं। / In conjugate multiplication, directly use the difference of squares.
Login to save your score, XP, coins and progress. Login
निम्नलिखित में से कौन-सा \(2+\sqrt{3}\) के बराबर है?
Which of the following is equal to \(2+\sqrt{3}\)?
#real-numbers
#equivalent-form
#rationalisation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\frac{1}{2-\sqrt{3}}\)
B \(\frac{1}{2+\sqrt{3}}\)
C \(2-\sqrt{3}\)
D \(\sqrt{3}-2\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2-\sqrt{3}}\)
Step 1
Concept
\(\frac{1}{2-\sqrt{3}}\) का हर परिमेय करने के लिए \(2+\sqrt{3}\) से गुणा करें। / Rationalise \(\frac{1}{2-\sqrt{3}}\) by multiplying by \(2+\sqrt{3}\).
Step 2
Why this answer is correct
हर (4-3=1) बनता है, इसलिए मान \(2+\sqrt{3}\) है। / The denominator becomes (4-3=1), so the value is \(2+\sqrt{3}\).
Step 3
Exam Tip
बराबर रूप पहचानने के लिए परिमेयकरण करें। / Use rationalisation to identify equivalent forms.
Login to save your score, XP, coins and progress. Login
यदि \(\sqrt{3}=1.732\) लगभग है, तो \(4\sqrt{3}\) का लगभग मान क्या होगा?
If \(\sqrt{3}=1.732\) approximately, what is the approximate value of \(4\sqrt{3}\)?
#real-numbers
#approximation
#sqrt3
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (6.928)
B (5.732)
C (4.732)
D (8.928)
Explanation opens after your attempt
Correct Answer
A. (6.928)
Step 1
Concept
दिए गए लगभग मान को (4) से गुणा करें। / Multiply the given approximate value by (4).
Step 2
Why this answer is correct
\(4\sqrt{3}\approx4\times1.732=6.928\)। / \(4\sqrt{3}\approx4\times1.732=6.928\).
Step 3
Exam Tip
अनुमान वाले प्रश्न में दिए गए मान का सीधा उपयोग करें। / In approximation questions, directly use the given value.
Login to save your score, XP, coins and progress. Login
कौन-सी संख्या \(6\sqrt{2}\) के बराबर है?
Which number is equal to \(6\sqrt{2}\)?
#real-numbers
#equivalent-radicals
#conversion
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{72}\)
B \(\sqrt{36}\)
C \(\sqrt{48}\)
D \(\sqrt{12}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{72}\)
Step 1
Concept
\(6\sqrt{2}=\sqrt{36}\sqrt{2}\)। / \(6\sqrt{2}=\sqrt{36}\sqrt{2}\).
Step 2
Why this answer is correct
यह \(\sqrt{72}\) के बराबर है। / This equals \(\sqrt{72}\).
Step 3
Exam Tip
बाहर का गुणांक अंदर ले जाने के लिए उसका वर्ग अंदर गुणा करें। / To move the outside coefficient inside, multiply by its square.
Login to save your score, XP, coins and progress. Login
यदि \(x=\sqrt{3}+\sqrt{27}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{3}+\sqrt{27}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt3
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(4\sqrt{3}\)
B \(\sqrt{30}\)
C \(3\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\)। / \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
\(x=\sqrt{3}+3\sqrt{3}=4\sqrt{3}\)। / \(x=\sqrt{3}+3\sqrt{3}=4\sqrt{3}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल रूप में बदलें। / Simplify radicals before adding them.
Login to save your score, XP, coins and progress. Login
कौन-सी संख्या \(\sqrt{6}\) और \(\sqrt{10}\) के बीच स्थित है?
Which number lies between \(\sqrt{6}\) and \(\sqrt{10}\)?
#real-numbers
#comparison
#between-roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3)
B (4)
C (2)
D \(\sqrt{12}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{6}\approx2.45\) और \(\sqrt{10}\approx3.16\)। / \(\sqrt{6}\approx2.45\) and \(\sqrt{10}\approx3.16\).
Step 2
Why this answer is correct
(3) इन दोनों के बीच आता है। / (3) lies between these two values.
Step 3
Exam Tip
तुलना के लिए लगभग मान या वर्ग करके जांच करें। / Use approximate values or squaring to compare.
Login to save your score, XP, coins and progress. Login
\(\sqrt{5}+\sqrt{20}+\sqrt{45}\) की प्रकृति क्या है?
What is the nature of \(\sqrt{5}+\sqrt{20}+\sqrt{45}\)?
#real-numbers
#irrational-expression
#radicals
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
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
कुल योग \(6\sqrt{5}\) है, जो अपरिमेय है। / The total is \(6\sqrt{5}\), which is irrational.
Step 3
Exam Tip
किसी अभिव्यक्ति की प्रकृति तय करने से पहले उसे सरल करें। / Simplify an expression before deciding its nature.
Login to save your score, XP, coins and progress. Login
यदि \(\sqrt{p}\) अपरिमेय है और (k) अशून्य परिमेय है, तो \(\frac{\sqrt{p}}{k}\) कैसी संख्या होगी?
If \(\sqrt{p}\) is irrational and (k) is a non-zero rational number, what type of number is \(\frac{\sqrt{p}}{k}\)?
#real-numbers
#irrational-rule
#division
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A परिमेय / Rational
B अपरिमेय / Irrational
C हमेशा पूर्णांक / Always integer
D हमेशा शून्य / Always zero
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
अशून्य परिमेय संख्या से भाग करने पर अपरिमेयता समाप्त नहीं होती। / Dividing by a non-zero rational number does not remove irrationality.
Step 2
Why this answer is correct
जैसे \(\frac{\sqrt{3}}{4}\) अपरिमेय रहता है। / For example, \(\frac{\sqrt{3}}{4}\) remains irrational.
Step 3
Exam Tip
यहां \(k\neq0\) जरूरी है क्योंकि शून्य से भाग संभव नहीं है। / The condition \(k\neq0\) is necessary because division by zero is not possible.
Login to save your score, XP, coins and progress. Login
\(\sqrt{216}+\sqrt{54}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{216}+\sqrt{54}\)?
#real-numbers
#radical-addition
#sqrt6
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(9\sqrt{6}\)
B \(6\sqrt{6}\)
C \(12\sqrt{6}\)
D \(\sqrt{270}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{6}\)
Step 1
Concept
\(\sqrt{216}=6\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\)। / \(\sqrt{216}=6\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\).
Step 2
Why this answer is correct
\(6\sqrt{6}+3\sqrt{6}=9\sqrt{6}\)। / \(6\sqrt{6}+3\sqrt{6}=9\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही उन्हें जोड़ें। / Add radicals only after they become like radicals.
Login to save your score, XP, coins and progress. Login
कौन-सा विकल्प परिमेय संख्या और अपरिमेय संख्या का ऐसा गुणनफल दिखाता है जो अपरिमेय है?
Which option shows the product of a rational number and an irrational number that is irrational?
#real-numbers
#rational-irrational-product
#concept
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(0\times\sqrt{11}\)
B \(4\times\sqrt{13}\)
C \(\sqrt{3}\times\sqrt{27}\)
D \(6\times5\)
Explanation opens after your attempt
Correct Answer
B. \(4\times\sqrt{13}\)
Step 1
Concept
(4) अशून्य परिमेय है और \(\sqrt{13}\) अपरिमेय है। / (4) is a non-zero rational number and \(\sqrt{13}\) is irrational.
Step 2
Why this answer is correct
\(4\sqrt{13}\) अपरिमेय रहेगा। / \(4\sqrt{13}\) remains irrational.
Step 3
Exam Tip
शून्य से गुणा करने का मामला अलग है, इसलिए अशून्य परिमेय पर ध्यान दें। / Multiplication by zero is a special case, so focus on non-zero rational factors.
Login to save your score, XP, coins and progress. Login
\(\sqrt{a}=12\) है। (a) के बारे में सही कथन कौन-सा है?
If \(\sqrt{a}=12\), which statement about (a) is correct?
#real-numbers
#square-root-equation
#perfect-square
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (a=24) और अपरिमेय है / (a=24) and is irrational
B (a=144) और पूर्ण वर्ग है / (a=144) and is a perfect square
C (a=12) और पूर्ण वर्ग नहीं है / (a=12) and is not a perfect square
D (a=72) और परिमेय नहीं है / (a=72) and is not rational
Explanation opens after your attempt
Correct Answer
B. (a=144) और पूर्ण वर्ग है / (a=144) and is a perfect square
Step 1
Concept
\(\sqrt{a}=12\) हो तो दोनों तरफ वर्ग करें। / If \(\sqrt{a}=12\), square both sides.
Step 2
Why this answer is correct
(a=144), और (144) पूर्ण वर्ग है। / (a=144), and (144) is a perfect square.
Step 3
Exam Tip
वर्गमूल समीकरण में मूल संख्या पाने के लिए वर्ग करें। / Square both sides in square-root equations to find the original number.
Login to save your score, XP, coins and progress. Login
निम्नलिखित में से कौन-सा परिणाम परिमेय नहीं है?
Which of the following results is not rational?
#real-numbers
#irrational-result
#mcq
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\sqrt{36}+\sqrt{64}\)
B \(\sqrt{10}\times\sqrt{40}\)
C \(\sqrt{3}+\sqrt{75}\)
D \(\sqrt{121}-\sqrt{100}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{3}+\sqrt{75}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\), इसलिए \(\sqrt{3}+\sqrt{75}=6\sqrt{3}\)। / \(\sqrt{75}=5\sqrt{3}\), so \(\sqrt{3}+\sqrt{75}=6\sqrt{3}\).
Step 2
Why this answer is correct
\(6\sqrt{3}\) अपरिमेय है, इसलिए परिमेय नहीं है। / \(6\sqrt{3}\) is irrational, so it is not rational.
Step 3
Exam Tip
हर विकल्प को सरल करने के बाद ही प्रकृति तय करें। / Simplify each option before deciding its nature.
Login to save your score, XP, coins and progress. Login
