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

Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Medium Class 9 Level 4

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Question 1/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(2^5 \times 2^3\) का मान क्या है?

What is the value of \(2^5 \times 2^3\)?

Explanation opens after your attempt

Correct Answer

A. 256

Explanation

Simple Explanation

समान आधार पर घात जोड़ते हैं। \(2^8=256\)। / Add exponents for the same base. \(2^8=256\).

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Question 2/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(5^6 \div 5^2\) का मान क्या है?

What is the value of \(5^6 \div 5^2\)?

Explanation opens after your attempt

Correct Answer

B. 625

Explanation

Simple Explanation

भाग में घात घटती है। \(5^4=625\)। / Subtract exponents in division. \(5^4=625\).

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Question 3/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

(\(3^2\)³) का मान क्या है?

What is the value of (\(3^2\)³)?

Explanation opens after your attempt

Correct Answer

C. 729

Explanation

Simple Explanation

घात की घात में गुणा करते हैं। \(3^6=729\)। / Multiply exponents in a power of a power. \(3^6=729\).

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Question 4/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(10^4 \div 10^4\) का मान क्या है?

What is the value of \(10^4 \div 10^4\)?

Explanation opens after your attempt

Correct Answer

D. 1

Explanation

Simple Explanation

समान संख्या का भागफल 1 होता है। \(10^0=1\)। / A number divided by itself is 1. \(10^0=1\).

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Question 5/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(7^2 \times 7^1\) का मान क्या है?

What is the value of \(7^2 \times 7^1\)?

Explanation opens after your attempt

Correct Answer

A. 343

Explanation

Simple Explanation

\(7^{2+1}=7^3\)। उत्तर 343 है। / \(7^{2+1}=7^3\). The answer is 343.

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Question 6/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(8^3 \div 8^1\) का मान क्या है?

What is the value of \(8^3 \div 8^1\)?

Explanation opens after your attempt

Correct Answer

B. 64

Explanation

Simple Explanation

\(8^{3-1}=8^2=64\)। नियम याद रखें। / \(8^{3-1}=8^2=64\). Remember the law.

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Question 7/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

(\(2^3\)²) का मान क्या है?

What is the value of (\(2^3\)²)?

Explanation opens after your attempt

Correct Answer

C. 64

Explanation

Simple Explanation

\(2^{3\times2}=2^6=64\)। / \(2^{3\times2}=2^6=64\).

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Question 8/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(9^0\) का मान क्या है?

What is the value of \(9^0\)?

Explanation opens after your attempt

Correct Answer

D. 1

Explanation

Simple Explanation

शून्य घात पर कोई भी अशून्य संख्या 1 होती है। / Any non-zero number raised to 0 equals 1.

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Question 9/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(6^2 \times 6^2\) का मान क्या है?

What is the value of \(6^2 \times 6^2\)?

Explanation opens after your attempt

Correct Answer

B. 1296

Explanation

Simple Explanation

\(6^4=1296\)। घात जोड़ें। / \(6^4=1296\). Add exponents.

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Question 10/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(2^4 \times 2^2\) का मान क्या है?

What is the value of \(2^4 \times 2^2\)?

Explanation opens after your attempt

Correct Answer

A. 64

Explanation

Simple Explanation

\(2^6=64\)। समान आधार पर घात जोड़ें। / \(2^6=64\). Add exponents for same base.

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Question 11/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(3^5 \div 3^3\) का मान क्या है?

What is the value of \(3^5 \div 3^3\)?

Explanation opens after your attempt

Correct Answer

B. 9

Explanation

Simple Explanation

\(3^{5-3}=3^2=9\)। / \(3^{5-3}=3^2=9\).

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Question 12/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

(\(5^2\)²) का मान क्या है?

What is the value of (\(5^2\)²)?

Explanation opens after your attempt

Correct Answer

C. 625

Explanation

Simple Explanation

\(5^{2\times2}=5^4=625\)। / \(5^{2\times2}=5^4=625\).

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Question 13/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(100^0\) का मान क्या है?

What is the value of \(100^0\)?

Explanation opens after your attempt

Correct Answer

D. 1

Explanation

Simple Explanation

शून्य घात का नियम लगाएँ। / Apply the zero exponent rule.

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Question 14/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

(\(2^2\)⁴) का मान क्या है?

What is the value of (\(2^2\)⁴)?

Explanation opens after your attempt

Correct Answer

C. 256

Explanation

Simple Explanation

\(2^{2\times4}=2^8=256\)। / \(2^{2\times4}=2^8=256\).

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Question 15/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(7^5 \div 7^5\) का मान क्या है?

What is the value of \(7^5 \div 7^5\)?

Explanation opens after your attempt

Correct Answer

D. 1

Explanation

Simple Explanation

समान पदों का भाग 1 होता है। / Division of equal terms gives 1.

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Question 16/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(3^2 \times 3^4\) का मान क्या है?

What is the value of \(3^2 \times 3^4\)?

Explanation opens after your attempt

Correct Answer

A. 729

Explanation

Simple Explanation

\(3^6=729\)। घात जोड़ें। / \(3^6=729\). Add exponents.

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Question 17/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(10^6 \div 10^3\) का मान क्या है?

What is the value of \(10^6 \div 10^3\)?

Explanation opens after your attempt

Correct Answer

B. 1000

Explanation

Simple Explanation

\(10^{6-3}=10^3=1000\)। / \(10^{6-3}=10^3=1000\).

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Question 18/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(12^2+2^2\) का मान क्या है?

What is the value of \(12^2+2^2\)?

Explanation opens after your attempt

Correct Answer

C. 148

Explanation

Simple Explanation

(144+4=148)। / (144+4=148).

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Question 19/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(14^2-5^2\) का मान क्या है?

What is the value of \(14^2-5^2\)?

Explanation opens after your attempt

Correct Answer

D. 171

Explanation

Simple Explanation

(196-25=171)। / (196-25=171).

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Question 20/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(2^3+2^4\) का मान क्या है?

What is the value of \(2^3+2^4\)?

Explanation opens after your attempt

Correct Answer

A. 24

Explanation

Simple Explanation

(8+16=24)। / (8+16=24).

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Question 21/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(5^3-5^2\) का मान क्या है?

What is the value of \(5^3-5^2\)?

Explanation opens after your attempt

Correct Answer

B. 100

Explanation

Simple Explanation

(125-25=100)। / (125-25=100).

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Question 22/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(2^5 \div 2^2\) का मान क्या है?

What is the value of \(2^5 \div 2^2\)?

Explanation opens after your attempt

Correct Answer

C. 8

Explanation

Simple Explanation

\(2^{5-2}=2^3=8\)। / \(2^{5-2}=2^3=8\).

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Question 23/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(9^3 \div 9^2\) का मान क्या है?

What is the value of \(9^3 \div 9^2\)?

Explanation opens after your attempt

Correct Answer

D. 9

Explanation

Simple Explanation

\(9^{3-2}=9\)। / \(9^{3-2}=9\).

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Question 24/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

(\(4^2\)²) का मान क्या है?

What is the value of (\(4^2\)²)?

Explanation opens after your attempt

Correct Answer

A. 256

Explanation

Simple Explanation

\(4^4=256\)। / \(4^4=256\).

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Question 25/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

(\(10^2\)²) का मान क्या है?

What is the value of (\(10^2\)²)?

Explanation opens after your attempt

Correct Answer

B. 10000

Explanation

Simple Explanation

\(10^4=10000\)। / \(10^4=10000\).

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Question 26/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(3^6\) का मान क्या है?

What is the value of \(3^6\)?

Explanation opens after your attempt

Correct Answer

B. 729

Explanation

Simple Explanation

\(3^6=729\)। / \(3^6=729\).

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Question 27/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(1^9\) का मान क्या है?

What is the value of \(1^9\)?

Explanation opens after your attempt

Correct Answer

A. 1

Explanation

Simple Explanation

1 की हर घात 1 होती है। / Any power of 1 is 1.

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Question 28/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(2^0+5^0\) का मान क्या है?

What is the value of \(2^0+5^0\)?

Explanation opens after your attempt

Correct Answer

B. 2

Explanation

Simple Explanation

\(2^0=1\) और \(5^0=1\)। योग 2 है। / \(2^0=1\) and \(5^0=1\). Sum is 2.

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Question 29/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(3^0+4^0+5^0\) का मान क्या है?

What is the value of \(3^0+4^0+5^0\)?

Explanation opens after your attempt

Correct Answer

C. 3

Explanation

Simple Explanation

तीनों का मान 1 है। योग 3 है। / Each term equals 1. Sum is 3.

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Question 30/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(2^4+3^3\) का मान क्या है?

What is the value of \(2^4+3^3\)?

Explanation opens after your attempt

Correct Answer

A. 43

Explanation

Simple Explanation

(16+27=43)। / (16+27=43).

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Question 31/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(5^3+2^5\) का मान क्या है?

What is the value of \(5^3+2^5\)?

Explanation opens after your attempt

Correct Answer

B. 157

Explanation

Simple Explanation

(125+32=157)। / (125+32=157).

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Question 32/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(10^2+6^2\) का मान क्या है?

What is the value of \(10^2+6^2\)?

Explanation opens after your attempt

Correct Answer

C. 136

Explanation

Simple Explanation

(100+36=136)। / (100+36=136).

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Question 33/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(15^2-9^2\) का मान क्या है?

What is the value of \(15^2-9^2\)?

Explanation opens after your attempt

Correct Answer

D. 144

Explanation

Simple Explanation

(225-81=144)। / (225-81=144).

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Question 34/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(4^3+3^2\) का मान क्या है?

What is the value of \(4^3+3^2\)?

Explanation opens after your attempt

Correct Answer

A. 73

Explanation

Simple Explanation

(64+9=73)। / (64+9=73).

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Question 35/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(7^2+8^2\) का मान क्या है?

What is the value of \(7^2+8^2\)?

Explanation opens after your attempt

Correct Answer

B. 113

Explanation

Simple Explanation

(49+64=113)। / (49+64=113).

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Question 36/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(9^2+4^2\) का मान क्या है?

What is the value of \(9^2+4^2\)?

Explanation opens after your attempt

Correct Answer

C. 97

Explanation

Simple Explanation

(81+16=97)। / (81+16=97).

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Question 37/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(8^2-3^2\) का मान क्या है?

What is the value of \(8^2-3^2\)?

Explanation opens after your attempt

Correct Answer

D. 55

Explanation

Simple Explanation

(64-9=55)। / (64-9=55).

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Question 38/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(2^8 \div 2^4\) का मान क्या है?

What is the value of \(2^8 \div 2^4\)?

Explanation opens after your attempt

Correct Answer

A. 16

Explanation

Simple Explanation

\(2^{8-4}=2^4=16\)। / \(2^{8-4}=2^4=16\).

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Question 39/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(3^7 \div 3^5\) का मान क्या है?

What is the value of \(3^7 \div 3^5\)?

Explanation opens after your attempt

Correct Answer

B. 9

Explanation

Simple Explanation

\(3^{7-5}=3^2=9\)। / \(3^{7-5}=3^2=9\).

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Question 40/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\((6^2)^2\) का मान क्या है?

What is the value of \((6^2)^2\)?

Explanation opens after your attempt

Correct Answer

C. 1296

Explanation

Simple Explanation

घातों के नियम के अनुसार \((a^m)^n = a^{mn}\)। इसलिए \((6^2)^2 = 6^{2\times2} = 6^4\)। अब \(6^2=36\) और \(36^2=1296\), अतः मान 1296 है। उत्तर के निकटवर्ती भ्रामक विकल्पों में से 36 वास्तव में \(6^2\) है और 216 \(6^3\) है; 256 किसी अन्य आधार/घात का परिणाम है। परीक्षा-सूचना: "power of a power" नियम याद रखें और बड़े घातों के लिए पहले छोटे घातों का मान निकालकर उसे गुणा/वर्ग करें। / Using the law of exponents \((a^m)^n = a^{mn}\), we have \((6^2)^2 = 6^{2\times2} = 6^4\). Compute stepwise: \(6^2=36\) and \(36^2=1296\), so the value is 1296. Distractors: 36 equals \(6^2\), 216 equals \(6^3\), and 256 is unrelated here. Exam tip: apply the power-of-a-power rule and simplify by computing smaller powers first if helpful.

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Question 41/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(50^0\) का मान क्या है?

What is the value of \(50^0\)?

Explanation opens after your attempt

Correct Answer

D. 1

Explanation

Simple Explanation

किसी भी अशून्य संख्या की शून्य घात 1 होती है। / Any non-zero number raised to zero equals 1.

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Question 42/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(17^2+3^2\) का मान क्या है?

What is the value of \(17^2+3^2\)?

Explanation opens after your attempt

Correct Answer

C. 298

Explanation

Simple Explanation

(289+9=298)। / (289+9=298).

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Question 43/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(18^2-7^2\) का मान क्या है?

What is the value of \(18^2-7^2\)?

Explanation opens after your attempt

Correct Answer

D. 275

Explanation

Simple Explanation

(324-49=275)। / (324-49=275).

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Question 44/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(4^6 \div 4^4\) का मान क्या है?

What is the value of \(4^6 \div 4^4\)?

Explanation opens after your attempt

Correct Answer

A. 16

Explanation

Simple Explanation

\(4^{6-4}=4^2=16\)। घातों के भाग का नियम लगाएँ। / \(4^{6-4}=4^2=16\). Apply the quotient law of exponents.

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Question 45/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

दिए गए अभिव्यक्ति (\(7^2\)²) का मान क्या है?

What is the value of the expression (\(7^2\)²)?

Explanation opens after your attempt

Correct Answer

A. 2401

Explanation

Simple Explanation

घात की घात (power of a power) के नियम के अनुसार, \((a^{m})^{n}=a^{m\times n}\)। इसलिए \((7^2)^2=7^{2\times2}=7^4=2401\)। विकल्प B (343) बराबर है \(7^3\) के, विकल्प C (49) बराबर है \(7^2\) के, और विकल्प D (2400) केवल संख्या के रूप में नजदीकी है पर गलत है। परीक्षा-सुझाव: घातों की घात में गुणन सोचें — जोड़ने या घटाने की बजाय घातों को गुणा करें। / Use the power-of-a-power rule: \((a^{m})^{n}=a^{m\times n}\). So \((7^2)^2=7^{2\times2}=7^4=2401\). Option B (343) equals \(7^3\), option C (49) equals \(7^2\), and option D (2400) is numerically close but incorrect. Exam tip: For \(a^m\)^n multiply the exponents m and n before evaluating the base.

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Question 46/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(5^2 \times 5^3\) का मान क्या है?

What is the value of \(5^2 \times 5^3\)?

Explanation opens after your attempt

Correct Answer

A. 3125

Explanation

Simple Explanation

\(5^{2+3}=5^5=3125\)। समान आधार पर घात जोड़ते हैं। / \(5^{2+3}=5^5=3125\). Add exponents for the same base.

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Question 47/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(6^4 \div 6^2\) का मान क्या है?

What is the value of \(6^4 \div 6^2\)?

Explanation opens after your attempt

Correct Answer

B. 36

Explanation

Simple Explanation

\(6^{4-2}=6^2=36\)। भाग में घात घटती है। / \(6^{4-2}=6^2=36\). Subtract exponents in division.

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Question 48/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

\(8^5 \div 8^3\) का मान क्या है?

What is the value of \(8^5 \div 8^3\)?

Explanation opens after your attempt

Correct Answer

D. 64

Explanation

Simple Explanation

\(8^{5-3}=8^2=64\)। भाग में घातें घटती हैं। / \(8^{5-3}=8^2=64\). Subtract exponents in division.

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Question 49/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

(\(3^3\)²) का मान क्या है?

What is the value of (\(3^3\)²)?

Explanation opens after your attempt

Correct Answer

A. 243

Explanation

Simple Explanation

\(3^{3\times2}=3^6=729\)। घात की घात में घातों का गुणा होता है। / \(3^{3\times2}=3^6=729\). Multiply exponents in a power of a power.

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Question 50/50 Medium Mathematics Number Systems Exponents Class 9 Level 4

यदि \(a^3=125\) हो तो (a) का मान क्या है?

If \(a^3=125\) then what is the value of (a)?

Explanation opens after your attempt

Correct Answer

C. 5

Explanation

Simple Explanation

\(125=5^3\) इसलिए (a=5)। घनमूल पहचानना सीखें। / \(125=5^3\), so (a=5). Learn to recognize perfect cubes.

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

\(2^5 \times 2^3\) का मान क्या है?

Simple Explanation

\(5^6 \div 5^2\) का मान क्या है?

Simple Explanation

(\(3^2\)3) का मान क्या है?

Simple Explanation

\(10^4 \div 10^4\) का मान क्या है?

Simple Explanation

\(7^2 \times 7^1\) का मान क्या है?

Simple Explanation

\(8^3 \div 8^1\) का मान क्या है?

Simple Explanation

(\(2^3\)2) का मान क्या है?

Simple Explanation

\(9^0\) का मान क्या है?

Simple Explanation

\(6^2 \times 6^2\) का मान क्या है?

Simple Explanation

\(2^4 \times 2^2\) का मान क्या है?

Simple Explanation

\(3^5 \div 3^3\) का मान क्या है?

Simple Explanation

(\(5^2\)2) का मान क्या है?

Simple Explanation

\(100^0\) का मान क्या है?

Simple Explanation

(\(2^2\)4) का मान क्या है?

Simple Explanation

\(7^5 \div 7^5\) का मान क्या है?

Simple Explanation

\(3^2 \times 3^4\) का मान क्या है?

Simple Explanation

\(10^6 \div 10^3\) का मान क्या है?

Simple Explanation

\(12^2+2^2\) का मान क्या है?

Simple Explanation

\(14^2-5^2\) का मान क्या है?

Simple Explanation

\(2^3+2^4\) का मान क्या है?

Simple Explanation

\(5^3-5^2\) का मान क्या है?

Simple Explanation

\(2^5 \div 2^2\) का मान क्या है?

Simple Explanation

\(9^3 \div 9^2\) का मान क्या है?

Simple Explanation

(\(4^2\)2) का मान क्या है?

Simple Explanation

(\(10^2\)2) का मान क्या है?

Simple Explanation

\(3^6\) का मान क्या है?

Simple Explanation

\(1^9\) का मान क्या है?

Simple Explanation

\(2^0+5^0\) का मान क्या है?

Simple Explanation

\(3^0+4^0+5^0\) का मान क्या है?

Simple Explanation

\(2^4+3^3\) का मान क्या है?

Simple Explanation

\(5^3+2^5\) का मान क्या है?

Simple Explanation

\(10^2+6^2\) का मान क्या है?

Simple Explanation

\(15^2-9^2\) का मान क्या है?

Simple Explanation

\(4^3+3^2\) का मान क्या है?

Simple Explanation

\(7^2+8^2\) का मान क्या है?

Simple Explanation

\(9^2+4^2\) का मान क्या है?

Simple Explanation

\(8^2-3^2\) का मान क्या है?

Simple Explanation

\(2^8 \div 2^4\) का मान क्या है?

Simple Explanation

\(3^7 \div 3^5\) का मान क्या है?

Simple Explanation

\((6^2)^2\) का मान क्या है?

(\(3^2\)³) का मान क्या है?

(\(2^3\)²) का मान क्या है?

(\(5^2\)²) का मान क्या है?

(\(2^2\)⁴) का मान क्या है?

(\(4^2\)²) का मान क्या है?

(\(10^2\)²) का मान क्या है?

दिए गए अभिव्यक्ति (\(7^2\)²) का मान क्या है?

(\(3^3\)²) का मान क्या है?