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Class 9 Mathematics - Number Systems - Proof of irrationality of square root 2 and square root 3 Expert Quiz

Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Expert Class 9 Level 3

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Question 1/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{12}+\sqrt{27}\) तो (x) का सरल रूप क्या है?

If \(x=\sqrt{12}+\sqrt{27}\), what is the simplified form of (x)?

Explanation opens after your attempt
Correct Answer

A. \(5\sqrt{3}\)

Explanation

Simple Explanation

\(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\)। समान मूलों को जोड़ें। / \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). Add like surds.

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Question 2/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(a=\sqrt{18}-\sqrt{8}\) तो (a) क्या है?

If \(a=\sqrt{18}-\sqrt{8}\), what is (a)?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\)

Explanation

Simple Explanation

\(3\sqrt{2}-2\sqrt{2}=\sqrt{2}\)। पहले सरल करें। / \(3\sqrt{2}-2\sqrt{2}=\sqrt{2}\). Simplify first.

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Question 3/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

किस भिन्न का दशमलव प्रसार असमाप्य आवर्ती है?

Which fraction has a non-terminating recurring decimal?

Explanation opens after your attempt
Correct Answer

B. \(\frac{7}{12}\)

Explanation

Simple Explanation

हर में 3 का गुणनखंड है। दशमलव आवर्ती होगा। / The denominator contains factor 3. The decimal will recur.

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Question 4/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{48}+\sqrt{75}\) का मान क्या है?

What is the value of \(\sqrt{48}+\sqrt{75}\)?

Explanation opens after your attempt
Correct Answer

C. \(13\sqrt{3}\)

Explanation

Simple Explanation

\(4\sqrt{3}+5\sqrt{3}=9\sqrt{3}\) नहीं। सही: \(\sqrt{48}=4\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), योग \(9\sqrt{3}\)। / Simplify each surd before adding. Always verify calculations.

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Question 5/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{2}\times\sqrt{50}\) तो (x) क्या है?

If \(x=\sqrt{2}\times\sqrt{50}\), what is (x)?

Explanation opens after your attempt
Correct Answer

B. 10

Explanation

Simple Explanation

\(\sqrt{100}=10\)। गुणन नियम लगाएँ। / \(\sqrt{100}=10\). Apply the multiplication rule.

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Question 6/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(a=\sqrt{5}\) और \(b=\sqrt{20}\) तो (a+b) क्या है?

If \(a=\sqrt{5}\) and \(b=\sqrt{20}\), what is (a+b)?

Explanation opens after your attempt
Correct Answer

C. \(5\sqrt{5}\)

Explanation

Simple Explanation

\(\sqrt{20}=2\sqrt{5}\)। योग \(3\sqrt{5}\) होगा। / \(\sqrt{20}=2\sqrt{5}\). Then add like surds.

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Question 7/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{7}\times\sqrt{63}\) का मान क्या है?

What is the value of \(\sqrt{7}\times\sqrt{63}\)?

Explanation opens after your attempt
Correct Answer

C. 21

Explanation

Simple Explanation

\(\sqrt{441}=21\)। पहले अंदर गुणा करें। / \(\sqrt{441}=21\). Multiply inside the root first.

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Question 8/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{81}-\sqrt{49}\) तो (x) क्या है?

If \(x=\sqrt{81}-\sqrt{49}\), what is (x)?

Explanation opens after your attempt
Correct Answer

B. 2

Explanation

Simple Explanation

(9-7=2)। मूलों का सही मान लें। / (9-7=2). Evaluate roots correctly.

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Question 9/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{98}-\sqrt{32}\) का मान क्या है?

What is the value of \(\sqrt{98}-\sqrt{32}\)?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\)

Explanation

Simple Explanation

\(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\)। पहले सरल करें। / \(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\). Simplify first.

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Question 10/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

कौन-सी संख्या \(\sqrt{50}\) के सबसे निकट है?

Which number is closest to \(\sqrt{50}\)?

Explanation opens after your attempt
Correct Answer

B. 7

Explanation

Simple Explanation

\(\sqrt{50}\approx7.07\)। अनुमान का प्रयोग करें। / \(\sqrt{50}\approx7.07\). Use estimation.

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Question 11/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{54}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{54}\)?

Explanation opens after your attempt
Correct Answer

B. \(3\sqrt{6}\)

Explanation

Simple Explanation

\(54=9\times6\)। \(\sqrt{9}=3\)। / \(54=9\times6\). \(\sqrt{9}=3\).

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Question 12/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(a=\sqrt{3}\) और \(b=\sqrt{12}\) तो (ab) क्या है?

If \(a=\sqrt{3}\) and \(b=\sqrt{12}\), what is (ab)?

Explanation opens after your attempt
Correct Answer

C. 6

Explanation

Simple Explanation

\(\sqrt{36}=6\)। गुणन नियम प्रयोग करें। / \(\sqrt{36}=6\). Use the multiplication rule.

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Question 13/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{169}+\sqrt{25}\) तो (x) क्या है?

If \(x=\sqrt{169}+\sqrt{25}\), what is (x)?

Explanation opens after your attempt
Correct Answer

C. 18

Explanation

Simple Explanation

(13+5=18)। वर्गमूल पहले निकालें। / (13+5=18). Evaluate roots first.

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Question 14/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

कौन-सा दशमलव समाप्य है?

Which decimal is terminating?

Explanation opens after your attempt
Correct Answer

B. \(\frac{11}{50}\)

Explanation

Simple Explanation

हर में केवल 2 और 5 हैं। / Denominator contains only 2 and 5.

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Question 15/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि (p) परिमेय और (q) अपरिमेय है तो (pq) क्या हो सकता है?

If (p) is rational and (q) is irrational then (pq) can be?

Explanation opens after your attempt
Correct Answer

C. परिमेय या अपरिमेय

Explanation

Simple Explanation

यदि (p=0) हो तो परिमेय मिलेगा। अन्यथा सामान्यतः अपरिमेय। / If (p=0), the product is rational. Otherwise usually irrational.

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Question 16/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{320}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{320}\)?

Explanation opens after your attempt
Correct Answer

B. \(8\sqrt{5}\)

Explanation

Simple Explanation

\(320=64\times5\)। \(\sqrt{64}=8\)। / \(320=64\times5\). \(\sqrt{64}=8\).

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Question 17/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{144}+\sqrt{196}\) तो (x) क्या है?

If \(x=\sqrt{144}+\sqrt{196}\), what is (x)?

Explanation opens after your attempt
Correct Answer

C. 26

Explanation

Simple Explanation

(12+14=26)। / (12+14=26).

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Question 18/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

कौन-सी संख्या \(\sqrt{20}\) और \(\sqrt{30}\) के बीच है?

Which number lies between \(\sqrt{20}\) and \(\sqrt{30}\)?

Explanation opens after your attempt
Correct Answer

B. 5

Explanation

Simple Explanation

\(\sqrt{20}\approx4.47\) और \(\sqrt{30}\approx5.48\)। / \(\sqrt{20}\approx4.47\) and \(\sqrt{30}\approx5.48\).

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Question 19/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{147}+\sqrt{75}\) का मान क्या है?

What is the value of \(\sqrt{147}+\sqrt{75}\)?

Explanation opens after your attempt
Correct Answer

C. \(12\sqrt{3}\)

Explanation

Simple Explanation

\(7\sqrt{3}+5\sqrt{3}=12\sqrt{3}\)। / \(7\sqrt{3}+5\sqrt{3}=12\sqrt{3}\).

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Question 20/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{256}\div\sqrt{16}\) तो (x) क्या है?

If \(x=\sqrt{256}\div\sqrt{16}\), what is (x)?

Explanation opens after your attempt
Correct Answer

C. 4

Explanation

Simple Explanation

\(16\div4=4\)। / \(16\div4=4\).

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Question 21/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{432}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{432}\)?

Explanation opens after your attempt
Correct Answer

A. \(12\sqrt{3}\)

Explanation

Simple Explanation

\(432=144\times3\)। / \(432=144\times3\).

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Question 22/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(a=\sqrt{8}\) और \(b=\sqrt{18}\) तो (a+b) क्या है?

If \(a=\sqrt{8}\) and \(b=\sqrt{18}\), what is (a+b)?

Explanation opens after your attempt
Correct Answer

B. \(5\sqrt{2}\)

Explanation

Simple Explanation

\(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\)। / \(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\).

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Question 23/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

किस संख्या का दशमलव समाप्य नहीं है?

Which number does not have a terminating decimal?

Explanation opens after your attempt
Correct Answer

C. \(\frac{13}{15}\)

Explanation

Simple Explanation

हर में 3 का गुणनखंड है। / The denominator contains factor 3.

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Question 24/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{225}-\sqrt{144}\) तो (x) क्या है?

If \(x=\sqrt{225}-\sqrt{144}\), what is (x)?

Explanation opens after your attempt
Correct Answer

C. 3

Explanation

Simple Explanation

(15-12=3)। / (15-12=3).

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Question 25/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{500}-\sqrt{125}\) का मान क्या है?

What is the value of \(\sqrt{500}-\sqrt{125}\)?

Explanation opens after your attempt
Correct Answer

A. \(5\sqrt{5}\)

Explanation

Simple Explanation

\(10\sqrt{5}-5\sqrt{5}=5\sqrt{5}\)। / \(10\sqrt{5}-5\sqrt{5}=5\sqrt{5}\).

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Question 26/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{324}+\sqrt{36}\) तो (x) क्या है?

If \(x=\sqrt{324}+\sqrt{36}\), what is (x)?

Explanation opens after your attempt
Correct Answer

C. 24

Explanation

Simple Explanation

(18+6=24)। / (18+6=24).

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Question 27/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{675}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{675}\)?

Explanation opens after your attempt
Correct Answer

A. \(15\sqrt{3}\)

Explanation

Simple Explanation

\(675=225\times3\)। / \(675=225\times3\).

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Question 28/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(a=\sqrt{27}\) और \(b=\sqrt{12}\) तो (a-b) क्या है?

If \(a=\sqrt{27}\) and \(b=\sqrt{12}\), what is (a-b)?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{3}\)

Explanation

Simple Explanation

\(3\sqrt{3}-2\sqrt{3}=\sqrt{3}\)। / \(3\sqrt{3}-2\sqrt{3}=\sqrt{3}\).

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Question 29/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

कौन-सा समुच्चय सभी वास्तविक संख्याओं को दर्शाता है?

Which set represents all real numbers?

Explanation opens after your attempt
Correct Answer

A. परिमेय और अपरिमेय का संघ

Explanation

Simple Explanation

वास्तविक = परिमेय ∪ अपरिमेय। / Real = Rational ∪ Irrational.

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Question 30/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{882}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{882}\)?

Explanation opens after your attempt
Correct Answer

C. \(21\sqrt{2}\)

Explanation

Simple Explanation

\(882=441\times2\)। / \(882=441\times2\).

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Question 31/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{400}-\sqrt{225}\) तो (x) क्या है?

If \(x=\sqrt{400}-\sqrt{225}\), what is (x)?

Explanation opens after your attempt
Correct Answer

B. 5

Explanation

Simple Explanation

(20-15=5)। / (20-15=5).

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Question 32/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

कौन-सी संख्या \(\sqrt{80}\) के सबसे निकट है?

Which number is closest to \(\sqrt{80}\)?

Explanation opens after your attempt
Correct Answer

B. 9

Explanation

Simple Explanation

\(\sqrt{80}\approx8.94\)। / \(\sqrt{80}\approx8.94\).

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Question 33/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{588}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{588}\)?

Explanation opens after your attempt
Correct Answer

C. \(14\sqrt{3}\)

Explanation

Simple Explanation

\(588=196\times3\)। / \(588=196\times3\).

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Question 34/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(a=\sqrt{50}\) और \(b=\sqrt{8}\) तो (a-b) क्या है?

If \(a=\sqrt{50}\) and \(b=\sqrt{8}\), what is (a-b)?

Explanation opens after your attempt
Correct Answer

A. \(3\sqrt{2}\)

Explanation

Simple Explanation

\(5\sqrt{2}-2\sqrt{2}=3\sqrt{2}\)। / \(5\sqrt{2}-2\sqrt{2}=3\sqrt{2}\).

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Question 35/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{968}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{968}\)?

Explanation opens after your attempt
Correct Answer

C. \(22\sqrt{2}\)

Explanation

Simple Explanation

\(968=484\times2\)। / \(968=484\times2\).

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Question 36/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{529}\div\sqrt{23}\) तो (x) क्या है?

If \(x=\sqrt{529}\div\sqrt{23}\), what is (x)?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{23}\)

Explanation

Simple Explanation

\(\sqrt{529}=23\)। फिर \(23/\sqrt{23}=\sqrt{23}\)। / \(\sqrt{529}=23\). Then \(23/\sqrt{23}=\sqrt{23}\).

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Question 37/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{726}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{726}\)?

Explanation opens after your attempt
Correct Answer

B. \(11\sqrt{6}\)

Explanation

Simple Explanation

\(726=121\times6\)। / \(726=121\times6\).

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Question 38/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{288}\) तो (x) का सरल रूप क्या है?

If \(x=\sqrt{288}\), what is the simplified form of (x)?

Explanation opens after your attempt
Correct Answer

B. \(12\sqrt{2}\)

Explanation

Simple Explanation

\(288=144\times2\)। \(\sqrt{144}=12\)। / \(288=144\times2\). \(\sqrt{144}=12\).

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Question 39/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

कौन-सी संख्या \(\sqrt{41}\) के सबसे निकट है?

Which number is closest to \(\sqrt{41}\)?

Explanation opens after your attempt
Correct Answer

B. 6

Explanation

Simple Explanation

\(\sqrt{41}\approx6.40\)। निकटतम पूर्णांक 6 है। / \(\sqrt{41}\approx6.40\). The nearest integer is 6.

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Question 40/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(a=\sqrt{32}\) और \(b=\sqrt{18}\) तो (a+b) क्या है?

If \(a=\sqrt{32}\) and \(b=\sqrt{18}\), what is (a+b)?

Explanation opens after your attempt
Correct Answer

C. \(7\sqrt{2}\)

Explanation

Simple Explanation

\(4\sqrt{2}+3\sqrt{2}=7\sqrt{2}\)। / \(4\sqrt{2}+3\sqrt{2}=7\sqrt{2}\).

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Question 41/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{847}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{847}\)?

Explanation opens after your attempt
Correct Answer

A. \(7\sqrt{17}\)

Explanation

Simple Explanation

\(847=49\times17\)। \(\sqrt{49}=7\)। / \(847=49\times17\). \(\sqrt{49}=7\).

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Question 42/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{625}-\sqrt{361}\) तो (x) क्या है?

If \(x=\sqrt{625}-\sqrt{361}\), what is (x)?

Explanation opens after your attempt
Correct Answer

C. 6

Explanation

Simple Explanation

(25-19=6)। वर्गमूल सही निकालें। / (25-19=6). Evaluate the roots correctly.

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Question 43/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(a=\sqrt{45}\) और \(b=\sqrt{20}\) तो (ab) क्या है?

If \(a=\sqrt{45}\) and \(b=\sqrt{20}\), what is (ab)?

Explanation opens after your attempt
Correct Answer

C. 30

Explanation

Simple Explanation

\(\sqrt{45\times20}=\sqrt{900}=30\)। / \(\sqrt{45\times20}=\sqrt{900}=30\).

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Question 44/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

कौन-सी संख्या \(\sqrt{70}\) और \(\sqrt{90}\) के बीच है?

Which number lies between \(\sqrt{70}\) and \(\sqrt{90}\)?

Explanation opens after your attempt
Correct Answer

C. 9

Explanation

Simple Explanation

\(\sqrt{70}\approx8.37\) और \(\sqrt{90}\approx9.49\)। / \(\sqrt{70}\approx8.37\) and \(\sqrt{90}\approx9.49\).

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Question 45/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{507}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{507}\)?

Explanation opens after your attempt
Correct Answer

C. \(13\sqrt{3}\)

Explanation

Simple Explanation

\(507=169\times3\)। \(\sqrt{169}=13\)। / \(507=169\times3\). \(\sqrt{169}=13\).

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Question 46/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(x=\sqrt{441}+\sqrt{324}\) तो (x) क्या है?

If \(x=\sqrt{441}+\sqrt{324}\), what is (x)?

Explanation opens after your attempt
Correct Answer

C. 39

Explanation

Simple Explanation

(21+18=39)। / (21+18=39).

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Question 47/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{1200}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{1200}\)?

Explanation opens after your attempt
Correct Answer

B. \(20\sqrt{3}\)

Explanation

Simple Explanation

\(1200=400\times3\)। \(\sqrt{400}=20\)। / \(1200=400\times3\). \(\sqrt{400}=20\).

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Question 48/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

यदि \(a=\sqrt{98}\) और \(b=\sqrt{50}\) तो (a-b) क्या है?

If \(a=\sqrt{98}\) and \(b=\sqrt{50}\), what is (a-b)?

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Correct Answer

B. \(2\sqrt{2}\)

Explanation

Simple Explanation

\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\)। इसलिए अंतर \(2\sqrt{2}\) है। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\). Hence the difference is \(2\sqrt{2}\).

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Question 49/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

कौन-सी संख्या \(\sqrt{95}\) के सबसे निकट है?

Which number is closest to \(\sqrt{95}\)?

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Correct Answer

C. 10

Explanation

Simple Explanation

\(\sqrt{95}\approx9.75\)। निकटतम पूर्णांक 10 है। / \(\sqrt{95}\approx9.75\). The nearest integer is 10.

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Question 50/50 Expert Mathematics Number Systems Real Numbers Class 9 Level 3

\(\sqrt{1452}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{1452}\)?

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Correct Answer

C. \(22\sqrt{3}\)

Explanation

Simple Explanation

\(1452=484\times3\)। \(\sqrt{484}=22\), इसलिए \(\sqrt{1452}=22\sqrt{3}\)। / \(\sqrt{1452}=22\sqrt{3}\) because \(1452=484\times3\) and \(\sqrt{484}=22\).

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