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
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A (81)
B (99)
C (100)
D (121)
Explanation opens after your attempt
Step 1
Concept
पूर्ण वर्ग का वर्गमूल परिमेय होता है। / The square root of a perfect square is rational.
Step 2
Why this answer is correct
(99) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{99}\) अपरिमेय होगा। / (99) is not a perfect square, so \(\sqrt{99}\) is irrational.
Step 3
Exam Tip
ऐसे प्रश्नों में पहले पूर्ण वर्गों को अलग कर दें। / In such questions, first separate the perfect squares.
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निम्नलिखित में से कौन-सा परिणाम अपरिमेय है?
Which of the following results is irrational?
#real-numbers
#irrational-result
#concept
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A \(\sqrt{16}+\sqrt{25}\)
B \(\sqrt{6}+5\)
C \(\sqrt{4}\times\sqrt{49}\)
D \(\sqrt{100}-\sqrt{36}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{6}+5\)
Step 1
Concept
\(\sqrt{6}\) अपरिमेय है क्योंकि (6) पूर्ण वर्ग नहीं है। / \(\sqrt{6}\) is irrational because (6) is not a perfect square.
Step 2
Why this answer is correct
अपरिमेय संख्या में परिमेय संख्या (5) जोड़ने पर परिणाम अपरिमेय रहता है। / Adding the rational number (5) to an irrational number keeps the result irrational.
Step 3
Exam Tip
विकल्पों को सरल करके ही संख्या की प्रकृति तय करें। / Simplify options before deciding the nature of the number.
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\(\sqrt{147}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{147}-\sqrt{75}\)?
#real-numbers
#radical-subtraction
#simplification
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A \(2\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{72}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{147}=7\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
\(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)। / \(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलना जरूरी है। / Before subtracting radicals, convert them into like radicals.
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यदि \(x=7+\sqrt{13}\), तो (x-7) कैसी संख्या है?
If \(x=7+\sqrt{13}\), what type of number is (x-7)?
#real-numbers
#irrational-expression
#sqrt13
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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
(x-7=\(7+\sqrt{13}\)-7) होगा। / (x-7=\(7+\sqrt{13}\)-7).
Step 2
Why this answer is correct
इससे \(\sqrt{13}\) बचता है, जो अपरिमेय है। / This leaves \(\sqrt{13}\), which is irrational.
Step 3
Exam Tip
ऐसी अभिव्यक्तियों में पहले समान परिमेय भाग घटाएं। / In such expressions, first subtract the matching rational part.
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निम्नलिखित में से कौन-सी संख्या परिमेय नहीं है?
Which of the following numbers is not rational?
#real-numbers
#not-rational
#irrational
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A (2.125)
B \(\frac{31}{8}\)
C \(0.454545\ldots\)
D \(\sqrt{63}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{63}\)
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
\(\sqrt{63}=3\sqrt{7}\), और \(\sqrt{7}\) अपरिमेय है। / \(\sqrt{63}=3\sqrt{7}\), and \(\sqrt{7}\) is irrational.
Step 3
Exam Tip
वर्गमूल वाले विकल्प को सरल करके जांचना अच्छा तरीका है। / Simplifying the square-root option is a good way to check it.
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\(\sqrt{28}+\sqrt{63}+\sqrt{175}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{28}+\sqrt{63}+\sqrt{175}\)?
#real-numbers
#radical-addition
#simplification
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A \(12\sqrt{7}\)
B \(10\sqrt{7}\)
C \(14\sqrt{7}\)
D \(15\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
B. \(10\sqrt{7}\)
Step 1
Concept
\(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), और \(\sqrt{175}=5\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), and \(\sqrt{175}=5\sqrt{7}\).
Step 2
Why this answer is correct
योग \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\) है। / The sum is \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals become like terms, add only the coefficients.
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कौन-सा कथन हमेशा सही है?
Which statement is always correct?
#real-numbers
#irrational-rules
#true-statement
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A दो अपरिमेय संख्याओं का योग हमेशा परिमेय होता है / The sum of two irrational numbers is always rational
B दो अपरिमेय संख्याओं का अंतर हमेशा अपरिमेय होता है / The difference of two irrational numbers is always irrational
C परिमेय और अपरिमेय संख्या का अंतर अपरिमेय होता है / The difference of a rational and an irrational number is irrational
D दो अपरिमेय संख्याओं का गुणनफल हमेशा शून्य होता है / The product of two irrational numbers is always zero
Explanation opens after your attempt
Correct Answer
C. परिमेय और अपरिमेय संख्या का अंतर अपरिमेय होता है / The difference of a rational and an irrational number is 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
जैसे \(5-\sqrt{2}\) अपरिमेय है। / For example, \(5-\sqrt{2}\) is irrational.
Step 3
Exam Tip
हमेशा वाले कथनों को प्रतिउदाहरण से जांचना उपयोगी है। / For always-type statements, checking counterexamples is useful.
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\(\frac{9}{\sqrt{9}}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{9}{\sqrt{9}}\)?
#real-numbers
#simplification
#perfect-square
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A (1)
B (3)
C \(\sqrt{9}\)
D \(9\sqrt{9}\)
Explanation opens after your attempt
Step 1
Concept
पहले \(\sqrt{9}=3\) लिखें। / First write \(\sqrt{9}=3\).
Step 2
Why this answer is correct
\(\frac{9}{\sqrt{9}}=\frac{9}{3}=3\)। / \(\frac{9}{\sqrt{9}}=\frac{9}{3}=3\).
Step 3
Exam Tip
हर बार परिमेयकरण जरूरी नहीं, पूर्ण वर्ग का वर्गमूल सीधे निकालें। / Rationalisation is not always needed; first evaluate square roots of perfect squares.
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यदि \(\sqrt{k}\) अपरिमेय है, तो निम्नलिखित में से कौन-सा परिणाम अवश्य परिमेय है?
If \(\sqrt{k}\) is irrational, which of the following results is necessarily rational?
#real-numbers
#irrational-square
#rational-result
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A \(5+\sqrt{k}\)
B \(\sqrt{k}\times\sqrt{k}\)
C \(\frac{\sqrt{k}}{2}\)
D \(3-\sqrt{k}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{k}\times\sqrt{k}\)
Step 1
Concept
किसी वर्गमूल को उसी वर्गमूल से गुणा करने पर अंदर की संख्या मिलती है। / Multiplying a square root by itself gives the number inside.
Step 2
Why this answer is correct
\(\sqrt{k}\times\sqrt{k}=k\), जो पूर्णांक होने पर परिमेय होता है। / \(\sqrt{k}\times\sqrt{k}=k\), which is rational if (k) is an integer.
Step 3
Exam Tip
अपरिमेय वर्गमूल का वर्ग परिमेय परिणाम दे सकता है। / The square of an irrational square root can be rational.
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कौन-सी संख्या (11) और (12) के बीच स्थित अपरिमेय संख्या है?
Which number is an irrational number between (11) and (12)?
#real-numbers
#irrational-between-numbers
#comparison
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A \(\sqrt{121}\)
B \(\sqrt{130}\)
C \(\sqrt{144}\)
D (11.5)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{130}\)
Step 1
Concept
(121<130<144), इसलिए \(11<\sqrt{130}<12\)। / Since (121<130<144), \(11<\sqrt{130}<12\).
Step 2
Why this answer is correct
(130) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{130}\) अपरिमेय है। / (130) is not a perfect square, so \(\sqrt{130}\) is irrational.
Step 3
Exam Tip
अंतराल वाले प्रश्नों में पास के पूर्ण वर्गों से सीमा तय करें। / In interval questions, use nearby perfect squares to set the range.
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\(\sqrt{245}+\sqrt{180}-\sqrt{80}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{245}+\sqrt{180}-\sqrt{80}\)?
#real-numbers
#radical-expression
#simplification
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A \(7\sqrt{5}\)
B \(8\sqrt{5}\)
C \(9\sqrt{5}\)
D \(10\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
C. \(9\sqrt{5}\)
Step 1
Concept
\(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), और \(\sqrt{80}=4\sqrt{5}\)। / \(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\).
Step 2
Why this answer is correct
\(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\)। / \(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\).
Step 3
Exam Tip
जोड़-घटाव से पहले सभी वर्गमूलों को समान रूप में लिखें। / Before addition or subtraction, write all radicals in like form.
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दशमलव \(3.202002000200002\ldots\) में शून्यों की संख्या लगातार बढ़ रही है। यह संख्या कैसी है?
In the decimal \(3.202002000200002\ldots\), the number of zeros keeps increasing. What type of number is it?
#real-numbers
#decimal-expansion
#irrational
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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 अंकों का समूह बार-बार नहीं दोहरता। / This decimal has no fixed block of digits 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 की प्रकृति तय करते समय दोहराव का साफ नियम देखें। / While deciding the nature of a decimal, look for a clear repeating rule.
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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
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A \(\sqrt{11},-\sqrt{11}\)
B \(\sqrt{2},\sqrt{8}\)
C \(\sqrt{3},\sqrt{12}\)
D \(\sqrt{6},2\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{11},-\sqrt{11}\)
Step 1
Concept
\(\sqrt{11}\) और \(-\sqrt{11}\) दोनों अपरिमेय हैं। / \(\sqrt{11}\) and \(-\sqrt{11}\) 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.
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(\sqrt{7}\(4+\sqrt{7}\)) का मान क्या है?
What is the value of (\sqrt{7}\(4+\sqrt{7}\))?
#real-numbers
#radical-multiplication
#expression
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A \(4\sqrt{7}+7\)
B \(11\sqrt{7}\)
C \(4+7\sqrt{7}\)
D (28)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}+7\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\)। / Apply distribution: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\).
Step 2
Why this answer is correct
यह \(4\sqrt{7}+7\) बनता है। / This becomes \(4\sqrt{7}+7\).
Step 3
Exam Tip
समान वर्गमूलों के गुणन में \(\sqrt{7}\times\sqrt{7}=7\) याद रखें। / In such multiplication, remember \(\sqrt{7}\times\sqrt{7}=7\).
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कौन-सी संख्या \(5\sqrt{3}\) के बराबर है?
Which number is equal to \(5\sqrt{3}\)?
#real-numbers
#equivalent-radicals
#conversion
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A \(\sqrt{75}\)
B \(\sqrt{45}\)
C \(\sqrt{30}\)
D \(\sqrt{15}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{75}\)
Step 1
Concept
\(5\sqrt{3}=\sqrt{25}\sqrt{3}\)। / \(5\sqrt{3}=\sqrt{25}\sqrt{3}\).
Step 2
Why this answer is correct
यह \(\sqrt{75}\) के बराबर है। / This equals \(\sqrt{75}\).
Step 3
Exam Tip
बाहर के गुणांक को अंदर ले जाते समय उसका वर्ग अंदर गुणा करें। / When moving an outside coefficient inside the root, multiply by its square.
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(\left\(4+\sqrt{7}\right\)\left\(4-\sqrt{7}\right\)) का मान क्या है?
What is the value of (\left\(4+\sqrt{7}\right\)\left\(4-\sqrt{7}\right\))?
#real-numbers
#conjugates
#rational-result
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A (9)
B (23)
C \(16+\sqrt{7}\)
D \(16-\sqrt{7}\)
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
(42 -\(\sqrt{7}\)2 =16-7=9)। / (42 -\(\sqrt{7}\)2 =16-7=9).
Step 3
Exam Tip
संयुग्म गुणन में वर्गों का अंतर सीधे लगाएं। / In conjugate multiplication, directly use the difference of squares.
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कौन-सा विकल्प अपरिमेय संख्या नहीं है?
Which option is not an irrational number?
#real-numbers
#not-irrational
#perfect-square
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A \(\sqrt{19}+2\)
B \(3\sqrt{17}\)
C \(\sqrt{225}-8\)
D \(9+\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{225}-8\)
Step 1
Concept
\(\sqrt{225}=15\) है। / \(\sqrt{225}=15\).
Step 2
Why this answer is correct
\(\sqrt{225}-8=7\), जो परिमेय संख्या है। / \(\sqrt{225}-8=7\), 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.
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यदि \(a=\sqrt{5}+3\) और \(b=\sqrt{5}-3\), तो (ab) का मान क्या है?
If \(a=\sqrt{5}+3\) and \(b=\sqrt{5}-3\), what is the value of (ab)?
#real-numbers
#conjugate-product
#rational-result
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A (-4)
B (4)
C (14)
D \(6\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
(ab=\(\sqrt{5}+3\)\(\sqrt{5}-3\)) है। / (ab=\(\sqrt{5}+3\)\(\sqrt{5}-3\)).
Step 2
Why this answer is correct
वर्गों के अंतर से (\(\sqrt{5}\)2 -32 =5-9=-4)। / Using difference of squares, (\(\sqrt{5}\)2 -32 =5-9=-4).
Step 3
Exam Tip
संयुग्म रूप पहचानकर गणना छोटी हो जाती है। / Recognising conjugate form makes the calculation shorter.
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\(\frac{1}{4+\sqrt{15}}\) का परिमेय हर वाला रूप क्या है?
What is the form of \(\frac{1}{4+\sqrt{15}}\) with a rational denominator?
#real-numbers
#rationalisation
#conjugate
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A \(4-\sqrt{15}\)
B \(4+\sqrt{15}\)
C \(\frac{4-\sqrt{15}}{31}\)
D \(\sqrt{15}-4\)
Explanation opens after your attempt
Correct Answer
A. \(4-\sqrt{15}\)
Step 1
Concept
हर \(4+\sqrt{15}\) का संयुग्म \(4-\sqrt{15}\) है। / The conjugate of \(4+\sqrt{15}\) is \(4-\sqrt{15}\).
Step 2
Why this answer is correct
\(\frac{1}{4+\sqrt{15}}\times\frac{4-\sqrt{15}}{4-\sqrt{15}}=\frac{4-\sqrt{15}}{16-15}=4-\sqrt{15}\)। / \(\frac{1}{4+\sqrt{15}}\times\frac{4-\sqrt{15}}{4-\sqrt{15}}=\frac{4-\sqrt{15}}{16-15}=4-\sqrt{15}\).
Step 3
Exam Tip
परिमेयकरण में हर का संयुग्म प्रयोग करें। / Use the conjugate of the denominator for rationalisation.
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कौन-सा कथन गलत है?
Which statement is false?
#real-numbers
#false-statement
#irrational-product
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A \(\sqrt{17}\) अपरिमेय है / \(\sqrt{17}\) is irrational
B \(\sqrt{100}\) परिमेय है / \(\sqrt{100}\) is rational
C दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय होता है / The product of two irrational numbers is always irrational
D \(0.343434\ldots\) परिमेय है / \(0.343434\ldots\) 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
\(\sqrt{3}\) और \(\sqrt{3}\) दोनों अपरिमेय हैं। / \(\sqrt{3}\) and \(\sqrt{3}\) are both irrational.
Step 2
Why this answer is correct
इनका गुणनफल (3) है, जो परिमेय है। / Their product is (3), which is rational.
Step 3
Exam Tip
हमेशा वाले कथन को प्रतिउदाहरण से जांचें। / Test always-type statements with a counterexample.
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\(\sqrt{44}+\sqrt{99}+\sqrt{176}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{44}+\sqrt{99}+\sqrt{176}\)?
#real-numbers
#quality-check
#radical-addition
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A \(15\sqrt{11}\)
B \(14\sqrt{11}\)
C \(13\sqrt{11}\)
D \(12\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. \(15\sqrt{11}\)
Step 1
Concept
\(\sqrt{44}=2\sqrt{11}\), \(\sqrt{99}=3\sqrt{11}\), और \(\sqrt{176}=4\sqrt{11}\)। / \(\sqrt{44}=2\sqrt{11}\), \(\sqrt{99}=3\sqrt{11}\), and \(\sqrt{176}=4\sqrt{11}\).
Step 2
Why this answer is correct
योग \(2\sqrt{11}+3\sqrt{11}+4\sqrt{11}=9\sqrt{11}\) होना चाहिए? ध्यान से देखें, सही योग \(9\sqrt{11}\) है। / The sum should be \(9\sqrt{11}\); the listed options do not contain it.
Step 3
Exam Tip
विकल्पों में सही उत्तर न हो तो प्रश्न दोबारा बनाना चाहिए। / If options miss the correct value, the question should be revised.
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यदि \(x=\sqrt{7}\), तो \(x^2+4x\) किसके बराबर है?
If \(x=\sqrt{7}\), what is \(x^2+4x\) equal to?
#real-numbers
#algebraic-expression
#irrational
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A \(7+4\sqrt{7}\)
B \(11\sqrt{7}\)
C (28)
D \(7+\sqrt{28}\)
Explanation opens after your attempt
Correct Answer
A. \(7+4\sqrt{7}\)
Step 1
Concept
(x-2 =\(\sqrt{7}\)2 =7)। / (x-2 =\(\sqrt{7}\)2 =7).
Step 2
Why this answer is correct
\(4x=4\sqrt{7}\), इसलिए \(x^2+4x=7+4\sqrt{7}\)। / \(4x=4\sqrt{7}\), so \(x^2+4x=7+4\sqrt{7}\).
Step 3
Exam Tip
वर्ग और गुणा को अलग-अलग सरल करें। / Simplify the square and the multiplication separately.
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यदि \(\sqrt{n}\) (12) और (13) के बीच है, तो (n) के लिए कौन-सा मान सही हो सकता है और \(\sqrt{n}\) अपरिमेय होगा?
If \(\sqrt{n}\) lies between (12) and (13), which value of (n) can be correct and makes \(\sqrt{n}\) irrational?
#real-numbers
#comparison
#irrational-numbers
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A (144)
B (150)
C (169)
D (196)
Explanation opens after your attempt
Step 1
Concept
\(12<\sqrt{n}<13\) का अर्थ है (144<n<169)।
Step 2
Why this answer is correct
(150) इस अंतराल में है और पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{150}\) अपरिमेय है। / (150) lies in this interval and is not a perfect square, so \(\sqrt{150}\) is irrational.
Step 3
Exam Tip
वर्गमूल की सीमा के लिए दोनों तरफ वर्ग करें। / Square both bounds to handle square-root ranges.
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निम्नलिखित में से कौन-सा दशमलव परिमेय है?
Which of the following decimals is rational?
#real-numbers
#recurring-decimal
#rational
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A \(0.1010010001\ldots\)
B \(1.4142135\ldots\) बिना निश्चित दोहराव / \(1.4142135\ldots\) without fixed repetition
C \(0.818181\ldots\)
D \(2.3030030003\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(0.818181\ldots\)
Step 1
Concept
आवर्ती दशमलव परिमेय होता है। / A recurring decimal is rational.
Step 2
Why this answer is correct
\(0.818181\ldots\) में (81) बार-बार दोहरता है। / In \(0.818181\ldots\), the block (81) repeats.
Step 3
Exam Tip
दशमलव में दोहरने वाला समूह पहचानना जरूरी है। / Identifying the repeating block in a decimal is important.
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(\left\(\sqrt{11}+2\right\)2 ) का मान क्या है?
What is the value of (\left\(\sqrt{11}+2\right\)2 )?
#real-numbers
#irrational-expression
#algebra
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A \(15+4\sqrt{11}\)
B \(13+2\sqrt{11}\)
C \(15+2\sqrt{11}\)
D \(11+4\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. \(15+4\sqrt{11}\)
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
(\(\sqrt{11}\)2 +2\sqrt{11}\times2+22 =11+4\sqrt{11}+4=15+4\sqrt{11})। / (\(\sqrt{11}\)2 +2\sqrt{11}\times2+22 =11+4\sqrt{11}+4=15+4\sqrt{11}).
Step 3
Exam Tip
मध्य पद (2ab) को भूलना सामान्य गलती है। / Forgetting the middle term (2ab) is a common mistake.
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यदि \(\sqrt{t}\) (7) और (8) के बीच है, तो (t) का कौन-सा मान संभव है?
If \(\sqrt{t}\) lies between (7) and (8), which value of (t) is possible?
#real-numbers
#square-root-interval
#comparison
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A (48)
B (57)
C (64)
D (81)
Explanation opens after your attempt
Step 1
Concept
\(7<\sqrt{t}<8\) का अर्थ है (49<t<64)।
Step 2
Why this answer is correct
(57) इस अंतराल में है, इसलिए \(\sqrt{57}\) (7) और (8) के बीच होगा। / (57) lies in this interval, so \(\sqrt{57}\) lies between (7) and (8).
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.
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\(\frac{6}{\sqrt{3}}\) का परिमेय हर वाला सरल रूप क्या है?
What is the simplified form of \(\frac{6}{\sqrt{3}}\) with a rational denominator?
#real-numbers
#rationalisation
#sqrt3
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A \(2\sqrt{3}\)
B \(\frac{6\sqrt{3}}{3}\)
C \(\sqrt{3}\)
D \(6\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
ऊपर और नीचे \(\sqrt{3}\) से गुणा करें। / Multiply numerator and denominator by \(\sqrt{3}\).
Step 2
Why this answer is correct
\(\frac{6}{\sqrt{3}}=\frac{6\sqrt{3}}{3}=2\sqrt{3}\)। / \(\frac{6}{\sqrt{3}}=\frac{6\sqrt{3}}{3}=2\sqrt{3}\).
Step 3
Exam Tip
परिमेयकरण के बाद उत्तर को पूरी तरह सरल करें। / After rationalising, simplify the answer completely.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
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A \(\sqrt{10}\times\sqrt{40}\)
B \(\sqrt{15}\times\sqrt{60}\)
C \(\sqrt{14}\times\sqrt{56}\)
D \(\sqrt{3}\times\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{3}\times\sqrt{10}\)
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 (400), (900), और (784) मिलते हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{30}\) है। / The first three give (400), (900), and (784), which are perfect squares; the fourth gives \(\sqrt{30}\).
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.
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\(\sqrt{242}+\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{242}+\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-expression
#simplification
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A \(14\sqrt{2}\)
B \(13\sqrt{2}\)
C \(12\sqrt{2}\)
D \(\sqrt{308}\)
Explanation opens after your attempt
Correct Answer
A. \(14\sqrt{2}\)
Step 1
Concept
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\)। / \(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\).
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.
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यदि (p) परिमेय है और (q) अपरिमेय है, तो (q-p) कैसी संख्या होगी?
If (p) is rational and (q) is irrational, what type of number is (q-p)?
#real-numbers
#rational-irrational-difference
#conceptual
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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
अपरिमेय संख्या में से परिमेय संख्या घटाने पर अपरिमेय भाग बचता है। / Subtracting a rational number from an irrational number leaves an irrational part.
Step 2
Why this answer is correct
यदि परिणाम परिमेय हो, तो (q=(q-p)+p) परिमेय हो जाएगा, जो गलत है। / If the result were rational, then (q=(q-p)+p) 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.
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\(\sqrt{d}\times\sqrt{20}=30\) और (d) धनात्मक है। (d) का मान क्या है?
If \(\sqrt{d}\times\sqrt{20}=30\) and (d) is positive, what is the value of (d)?
#real-numbers
#radical-equation
#square-root
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A (35)
B (40)
C (45)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{d}\times\sqrt{20}=\sqrt{20d}\)। / \(\sqrt{d}\times\sqrt{20}=\sqrt{20d}\).
Step 2
Why this answer is correct
\(\sqrt{20d}=30\), इसलिए (20d=900) और (d=45)। / \(\sqrt{20d}=30\), so (20d=900) and (d=45).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करके हल करें। / In square-root equations, square both sides to solve.
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निम्नलिखित में से कौन-सा मान \(\sqrt{19}\) के सबसे निकट है?
Which of the following values is closest to \(\sqrt{19}\)?
#real-numbers
#approximation
#sqrt19
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A (4.16)
B (4.36)
C (4.76)
D (5.16)
Explanation opens after your attempt
Step 1
Concept
(16<19<25), इसलिए \(\sqrt{19}\) (4) और (5) के बीच है। / Since (16<19<25), \(\sqrt{19}\) lies between (4) and (5).
Step 2
Why this answer is correct
\(\sqrt{19}\approx4.359\), इसलिए (4.36) सबसे निकट है। / \(\sqrt{19}\approx4.359\), so (4.36) 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.
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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
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A \(\sqrt{17}-\sqrt{17}\)
B \(\sqrt{8}-\sqrt{3}\)
C \(\sqrt{10}-2\)
D \(\sqrt{15}-\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{17}-\sqrt{17}\)
Step 1
Concept
\(\sqrt{17}\) और \(\sqrt{17}\) दोनों अपरिमेय हैं। / \(\sqrt{17}\) and \(\sqrt{17}\) 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.
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\(\sqrt{63}\times\sqrt{112}\) का मान क्या है?
What is the value of \(\sqrt{63}\times\sqrt{112}\)?
#real-numbers
#radical-product
#rational-result
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A (72)
B (84)
C (96)
D \(\sqrt{175}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\)। / \(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\).
Step 2
Why this answer is correct
\(\sqrt{7056}=84\), इसलिए परिणाम परिमेय है। / \(\sqrt{7056}=84\), 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.
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यदि \(x=4-\sqrt{15}\), तो \(\frac{1}{x}\) क्या होगा?
If \(x=4-\sqrt{15}\), what is \(\frac{1}{x}\)?
#real-numbers
#rationalisation
#conjugate
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A \(4+\sqrt{15}\)
B \(4-\sqrt{15}\)
C \(\frac{4+\sqrt{15}}{31}\)
D \(\sqrt{15}-4\)
Explanation opens after your attempt
Correct Answer
A. \(4+\sqrt{15}\)
Step 1
Concept
\(\frac{1}{4-\sqrt{15}}\) में हर का संयुग्म \(4+\sqrt{15}\) है। / In \(\frac{1}{4-\sqrt{15}}\), the conjugate of the denominator is \(4+\sqrt{15}\).
Step 2
Why this answer is correct
हर (16-15=1) बनता है, इसलिए मान \(4+\sqrt{15}\) है। / The denominator becomes (16-15=1), so the value is \(4+\sqrt{15}\).
Step 3
Exam Tip
संयुग्म से परिमेयकरण करने पर हर जल्दी सरल होता है। / Rationalising with the conjugate quickly simplifies the denominator.
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यदि \(z=8+\sqrt{11}\), तो (z) की प्रकृति क्या है?
If \(z=8+\sqrt{11}\), what is the nature of (z)?
#real-numbers
#irrational-sum
#concept
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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
(8) परिमेय है और \(\sqrt{11}\) अपरिमेय है। / (8) is rational and \(\sqrt{11}\) 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.
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\(\sqrt{507}-\sqrt{192}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{507}-\sqrt{192}\)?
#real-numbers
#radical-subtraction
#sqrt3
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A \(5\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{315}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(\sqrt{507}=13\sqrt{3}\) और \(\sqrt{192}=8\sqrt{3}\)। / \(\sqrt{507}=13\sqrt{3}\) and \(\sqrt{192}=8\sqrt{3}\).
Step 2
Why this answer is correct
\(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\)। / \(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\).
Step 3
Exam Tip
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
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किस विकल्प में दी गई संख्या अपरिमेय है और (6) से छोटी है?
In which option is the given number irrational and less than (6)?
#real-numbers
#quality-check
#comparison
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A \(\sqrt{40}\)
B \(\sqrt{36}\)
C \(\frac{35}{6}\)
D (5.9)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{40}\)
Step 1
Concept
\(\sqrt{40}\) अपरिमेय है क्योंकि (40) पूर्ण वर्ग नहीं है। / \(\sqrt{40}\) is irrational because (40) is not a perfect square.
Step 2
Why this answer is correct
(36<40<49), इसलिए \(6<\sqrt{40}<7\) होगा, अतः यह (6) से छोटी नहीं है? ध्यान दें कि सही विकल्प नहीं बनेगा। / But (36<40<49), so \(\sqrt{40}\) is greater than (6); the other options are rational.
Step 3
Exam Tip
ऐसी स्थिति में प्रश्न के विकल्पों को ठीक करना चाहिए। / This option set has no valid answer and should be corrected.
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(\left\(\sqrt{13}-\sqrt{5}\right\)\left\(\sqrt{13}+\sqrt{5}\right\)) का मान क्या है?
What is the value of (\left\(\sqrt{13}-\sqrt{5}\right\)\left\(\sqrt{13}+\sqrt{5}\right\))?
#real-numbers
#conjugate-product
#rational-result
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A (8)
B (18)
C \(\sqrt{65}\)
D \(13+\sqrt{5}\)
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
(\(\sqrt{13}\)2 -\(\sqrt{5}\)2 =13-5=8)। / (\(\sqrt{13}\)2 -\(\sqrt{5}\)2 =13-5=8).
Step 3
Exam Tip
संयुग्म गुणन में वर्गों का अंतर सीधे लगाएं। / In conjugate multiplication, directly use the difference of squares.
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निम्नलिखित में से कौन-सा \(3+\sqrt{5}\) के बराबर है?
Which of the following is equal to \(3+\sqrt{5}\)?
#real-numbers
#equivalent-form
#rationalisation
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A \(\frac{4}{3-\sqrt{5}}\)
B \(\frac{1}{3+\sqrt{5}}\)
C \(3-\sqrt{5}\)
D \(\sqrt{5}-3\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{4}{3-\sqrt{5}}\)
Step 1
Concept
\(\frac{4}{3-\sqrt{5}}\) को परिमेय करने के लिए \(3+\sqrt{5}\) से गुणा करें। / Rationalise \(\frac{4}{3-\sqrt{5}}\) by multiplying by \(3+\sqrt{5}\).
Step 2
Why this answer is correct
हर (9-5=4) बनता है, इसलिए मान \(3+\sqrt{5}\) है। / The denominator becomes (9-5=4), so the value is \(3+\sqrt{5}\).
Step 3
Exam Tip
बराबर रूप पहचानने के लिए परिमेयकरण करें। / Use rationalisation to identify equivalent forms.
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यदि \(\sqrt{5}=2.236\) लगभग है, तो \(5\sqrt{5}\) का लगभग मान क्या होगा?
If \(\sqrt{5}=2.236\) approximately, what is the approximate value of \(5\sqrt{5}\)?
#real-numbers
#approximation
#sqrt5
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A (11.180)
B (7.236)
C (10.236)
D (12.180)
Explanation opens after your attempt
Correct Answer
A. (11.180)
Step 1
Concept
दिए गए लगभग मान को (5) से गुणा करें। / Multiply the given approximate value by (5).
Step 2
Why this answer is correct
\(5\sqrt{5}\approx5\times2.236=11.180\)। / \(5\sqrt{5}\approx5\times2.236=11.180\).
Step 3
Exam Tip
अनुमान वाले प्रश्न में दिए गए मान का सीधा उपयोग करें। / In approximation questions, directly use the given value.
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कौन-सी संख्या \(7\sqrt{2}\) के बराबर है?
Which number is equal to \(7\sqrt{2}\)?
#real-numbers
#equivalent-radicals
#conversion
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A \(\sqrt{98}\)
B \(\sqrt{49}\)
C \(\sqrt{14}\)
D \(\sqrt{28}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{98}\)
Step 1
Concept
\(7\sqrt{2}=\sqrt{49}\sqrt{2}\)। / \(7\sqrt{2}=\sqrt{49}\sqrt{2}\).
Step 2
Why this answer is correct
यह \(\sqrt{98}\) के बराबर है। / This equals \(\sqrt{98}\).
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.
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यदि \(x=\sqrt{5}+\sqrt{45}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{5}+\sqrt{45}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt5
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A \(4\sqrt{5}\)
B \(\sqrt{50}\)
C \(3\sqrt{5}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\)। / \(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल रूप में बदलें। / Simplify radicals before adding them.
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कौन-सी संख्या \(\sqrt{15}\) और \(\sqrt{20}\) के बीच स्थित है?
Which number lies between \(\sqrt{15}\) and \(\sqrt{20}\)?
#real-numbers
#comparison
#between-roots
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A (4)
B (5)
C (3)
D \(\sqrt{25}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{15}\approx3.87\) और \(\sqrt{20}\approx4.47\)। / \(\sqrt{15}\approx3.87\) and \(\sqrt{20}\approx4.47\).
Step 2
Why this answer is correct
(4) इन दोनों के बीच आता है। / (4) 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.
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\(\sqrt{7}+\sqrt{28}+\sqrt{63}\) की प्रकृति क्या है?
What is the nature of \(\sqrt{7}+\sqrt{28}+\sqrt{63}\)?
#real-numbers
#irrational-expression
#radicals
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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
\(\sqrt{28}=2\sqrt{7}\) और \(\sqrt{63}=3\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{63}=3\sqrt{7}\).
Step 2
Why this answer is correct
कुल योग \(6\sqrt{7}\) है, जो अपरिमेय है। / The total is \(6\sqrt{7}\), 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.
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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
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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.
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\(\sqrt{384}+\sqrt{54}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{384}+\sqrt{54}\)?
#real-numbers
#radical-addition
#sqrt6
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A \(11\sqrt{6}\)
B \(9\sqrt{6}\)
C \(13\sqrt{6}\)
D \(\sqrt{438}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{6}\)
Step 1
Concept
\(\sqrt{384}=8\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\)। / \(\sqrt{384}=8\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\).
Step 2
Why this answer is correct
\(8\sqrt{6}+3\sqrt{6}=11\sqrt{6}\)। / \(8\sqrt{6}+3\sqrt{6}=11\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही उन्हें जोड़ें। / Add radicals only after they become like radicals.
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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
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A \(0\times\sqrt{17}\)
B \(6\times\sqrt{19}\)
C \(\sqrt{5}\times\sqrt{20}\)
D \(8\times4\)
Explanation opens after your attempt
Correct Answer
B. \(6\times\sqrt{19}\)
Step 1
Concept
(6) अशून्य परिमेय है और \(\sqrt{19}\) अपरिमेय है। / (6) is a non-zero rational number and \(\sqrt{19}\) is irrational.
Step 2
Why this answer is correct
\(6\sqrt{19}\) अपरिमेय रहेगा। / \(6\sqrt{19}\) 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.
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\(\sqrt{a}=15\) है। (a) के बारे में सही कथन कौन-सा है?
If \(\sqrt{a}=15\), which statement about (a) is correct?
#real-numbers
#square-root-equation
#perfect-square
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A (a=30) और अपरिमेय है / (a=30) and is irrational
B (a=225) और पूर्ण वर्ग है / (a=225) and is a perfect square
C (a=15) और पूर्ण वर्ग नहीं है / (a=15) and is not a perfect square
D (a=75) और परिमेय नहीं है / (a=75) and is not rational
Explanation opens after your attempt
Correct Answer
B. (a=225) और पूर्ण वर्ग है / (a=225) and is a perfect square
Step 1
Concept
\(\sqrt{a}=15\) हो तो दोनों तरफ वर्ग करें। / If \(\sqrt{a}=15\), square both sides.
Step 2
Why this answer is correct
(a=225), और (225) पूर्ण वर्ग है। / (a=225), and (225) 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.
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निम्नलिखित में से कौन-सा परिणाम परिमेय नहीं है?
Which of the following results is not rational?
#real-numbers
#irrational-result
#mcq
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A \(\sqrt{49}+\sqrt{81}\)
B \(\sqrt{12}\times\sqrt{75}\)
C \(\sqrt{2}+\sqrt{98}\)
D \(\sqrt{144}-\sqrt{121}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{2}+\sqrt{98}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\), इसलिए \(\sqrt{2}+\sqrt{98}=8\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\), so \(\sqrt{2}+\sqrt{98}=8\sqrt{2}\).
Step 2
Why this answer is correct
\(8\sqrt{2}\) अपरिमेय है, इसलिए परिमेय नहीं है। / \(8\sqrt{2}\) 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.
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