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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 1

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Question 1/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

( \(5-\sqrt{6}\)2 ) का सरल रूप क्या है?

What is the simplified form of ( \(5-\sqrt{6}\)2 )?

Explanation opens after your attempt
Correct Answer

A. \(31-10\sqrt{6}\)

Explanation

Simple Explanation

( (a-b)2=a-2-2ab+b-2 ) से \(25-10\sqrt{6}+6=31-10\sqrt{6}\) मिलता है। संकेतों पर विशेष ध्यान दें। / Using ( (a-b)2=a-2-2ab+b-2 ), we get \(25-10\sqrt{6}+6=31-10\sqrt{6}\). Pay special attention to signs.

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Question 2/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

( \(4+\sqrt{11}\)\(4-\sqrt{11}\) ) का मान क्या है?

What is the value of ( \(4+\sqrt{11}\)\(4-\sqrt{11}\) )?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

यह संयुग्मी गुणन है। (42-\(\sqrt{11}\)2=16-11=5) होगा। / This is conjugate multiplication. (42-\(\sqrt{11}\)2=16-11=5).

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Question 3/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

\( \sqrt{27}\times\sqrt{12} \) का मान क्या है?

What is the value of \( \sqrt{27}\times\sqrt{12} \)?

Explanation opens after your attempt
Correct Answer

A. (18)

Explanation

Simple Explanation

\( \sqrt{27}\times\sqrt{12}=\sqrt{324}=18 \)। गुणा में करणी के अंदर की संख्याएँ गुणा करें। / \( \sqrt{27}\times\sqrt{12}=\sqrt{324}=18 \). In multiplication, multiply the numbers inside the radicals.

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Question 4/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

\( \sqrt{90}\div\sqrt{10} \) का मान क्या है?

What is the value of \( \sqrt{90}\div\sqrt{10} \)?

Explanation opens after your attempt
Correct Answer

B. (3)

Explanation

Simple Explanation

\( \frac{\sqrt{90}}{\sqrt{10}}=\sqrt{9}=3 \)। करणी भाग में अंदर की संख्याओं का भाग लें। / \( \frac{\sqrt{90}}{\sqrt{10}}=\sqrt{9}=3 \). In radical division, divide the radicands.

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Question 5/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

\( \sqrt{0.81}+\sqrt{0.04} \) का मान क्या है?

What is the value of \( \sqrt{0.81}+\sqrt{0.04} \)?

Explanation opens after your attempt
Correct Answer

B. (1.1)

Explanation

Simple Explanation

\( \sqrt{0.81}=0.9 \) और \( \sqrt{0.04}=0.2 \) है। योग (1.1) होगा। / \( \sqrt{0.81}=0.9 \) and \( \sqrt{0.04}=0.2 \). The sum is (1.1).

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Question 6/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

\( \sqrt{\frac{9}{16}}+\sqrt{\frac{25}{36}} \) का मान क्या है?

What is the value of \( \sqrt{\frac{9}{16}}+\sqrt{\frac{25}{36}} \)?

Explanation opens after your attempt
Correct Answer

A. \( \frac{19}{12} \)

Explanation

Simple Explanation

पहला पद \( \frac{3}{4} \) और दूसरा \( \frac{5}{6} \) है। योग \( \frac{9}{12}+\frac{10}{12}=\frac{19}{12} \) मिलता है। / The first term is \( \frac{3}{4} \) and the second is \( \frac{5}{6} \). The sum is \( \frac{9}{12}+\frac{10}{12}=\frac{19}{12} \).

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Question 7/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

\( \sqrt{\frac{49}{100}}-\sqrt{\frac{4}{25}} \) का मान क्या है?

What is the value of \( \sqrt{\frac{49}{100}}-\sqrt{\frac{4}{25}} \)?

Explanation opens after your attempt
Correct Answer

B. \( \frac{3}{10} \)

Explanation

Simple Explanation

\( \sqrt{\frac{49}{100}}=\frac{7}{10} \) और \( \sqrt{\frac{4}{25}}=\frac{2}{5} \) है। अंतर \( \frac{3}{10} \) है। / \( \sqrt{\frac{49}{100}}=\frac{7}{10} \) and \( \sqrt{\frac{4}{25}}=\frac{2}{5} \). The difference is \( \frac{3}{10} \).

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Question 8/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

\( \sqrt{26} \) किस दो पूर्णांकों के बीच है?

Between which two integers does \( \sqrt{26} \) lie?

Explanation opens after your attempt
Correct Answer

B. (5) और (6)(5) and (6)

Explanation

Simple Explanation

\(5^2=25\) और \(6^2=36\) है इसलिए \( \sqrt{26} \) (5) और (6) के बीच है। निकट पूर्ण वर्गों की तुलना करें। / \(5^2=25\) and \(6^2=36\), so \( \sqrt{26} \) lies between (5) and (6). Compare nearby perfect squares.

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Question 9/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

\( \sqrt{53} \) का स्थान किन दो पूर्णांकों के बीच होगा?

Between which two integers will \( \sqrt{53} \) lie?

Explanation opens after your attempt
Correct Answer

C. (7) और (8)(7) and (8)

Explanation

Simple Explanation

\(7^2=49\) और \(8^2=64\) है इसलिए \( \sqrt{53} \) (7) और (8) के बीच है। वर्ग करके सीमा जाँचें। / \(7^2=49\) and \(8^2=64\), so \( \sqrt{53} \) lies between (7) and (8). Check limits by squaring.

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Question 10/10 Medium Mathematics Number Systems Real Numbers Class 9 Level 1

\( |-\sqrt{49}+3| \) का मान क्या है?

What is the value of \( |-\sqrt{49}+3| \)?

Explanation opens after your attempt
Correct Answer

A. (4)

Explanation

Simple Explanation

\( -\sqrt{49}+3=-7+3=-4 \) है और ( |-4|=4 )। निरपेक्ष मान दूरी देता है। / \( -\sqrt{49}+3=-7+3=-4 \) and ( |-4|=4 ). Absolute value gives distance.

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