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 5

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Question 1/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

यदि \(x^2=144\) तो धनात्मक (x) क्या है?

If \(x^2=144\) then what is the positive value of (x)?

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Correct Answer

A. 12

Explanation

Simple Explanation

\(12^2=144\)। वर्गमूल पहचानें। / \(12^2=144\). Recognize perfect squares.

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Question 2/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

यदि \(a^3=216\) तो (a) क्या है?

If \(a^3=216\) then what is (a)?

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Correct Answer

B. 6

Explanation

Simple Explanation

\(6^3=216\)। घनमूल लें। / \(6^3=216\). Take the cube root.

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Question 3/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

निम्नलिखित का मान क्या है: \((17^2 - 8^2)\)?

Find the value of \((17^2 - 8^2)\).

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Correct Answer

C. 225

Explanation

Simple Explanation

कारण: किसी भी दो संख्याओं के वर्गों का अन्तर नीचे के सूत्र से सरल होता है: \(a^2 - b^2 = (a-b)(a+b)\). यहाँ \(a=17\) और \(b=8\)। इसलिए \((17^2 - 8^2) = (17-8)(17+8) = 9\times25 = 225\). गलत विकल्पों का संक्षिप्त विश्लेषण: विकल्प A (81) आम गलती है जब कोई विद्यार्थी गलती से \((17-8)^2\) निकाल देता है; विकल्प B (353) तब बनता है जब \(17^2 + 8^2\) लिया जाए; विकल्प D (233) एक साधारण अंकगणितीय त्रुटि है (जैसे 289-56 या अशुद्ध घटाव). परीक्षा सुझाव: तेज़ गणना के लिए \(a^2-b^2\) पहचानें और इसे \((a-b)(a+b)\) में बदलकर गुणा करें। / Reason: Use the difference of squares identity \(a^2 - b^2 = (a-b)(a+b)\). With \(a=17\) and \(b=8\), \((17^2 - 8^2) = (17-8)(17+8) = 9\times25 = 225\). Brief notes on wrong options: option A (81) results from the mistake of computing \((17-8)^2\); option B (353) is the sum \(17^2+8^2\); option D (233) is a likely arithmetic subtraction error. Exam tip: Recognise and apply the identity \(a^2-b^2=(a-b)(a+b)\) to simplify such problems quickly and avoid careless subtraction mistakes.

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Question 4/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

18² + 19² का मान क्या है?

What is the value of 18² + 19²?

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Correct Answer

C. 685

Explanation

Simple Explanation

18² = 324 और 19² = 361, अतः 324 + 361 = 685। वैकल्पिक रूप से लगातार संख्याओं के लिए सामान्य सूत्र उपयोग करें: \(n^2+(n+1)^2=2n(n+1)+1\)। यहाँ n = 18 है, इसलिए \(2\times18\times19+1=684+1=685\)। सबसे नजदीकी भ्रांतिकर विकल्प (जैसे 675) केवल अंकों की गिनती में त्रुटि से बनता है। परीक्षा टिप: लगातार पूर्णांकों के वर्ग जोड़ने के लिए उपरोक्त सूत्र याद रखें ताकि गलतियाँ कम हों। / 18² = 324 and 19² = 361, so 324 + 361 = 685. Alternatively use the formula for consecutive squares: \(n^2+(n+1)^2=2n(n+1)+1\). With n = 18, \(2\times18\times19+1=684+1=685\). A close distractor like 675 typically arises from an arithmetic slip computing one of the squares. Exam tip: use the consecutive-square formula to avoid calculation errors under time pressure.

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Question 5/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

यदि \(b^2=225\) तो धनात्मक (b) क्या है?

If \(b^2=225\) then what is the positive value of (b)?

Explanation opens after your attempt

Correct Answer

A. 15

Explanation

Simple Explanation

\(15^2=225\)। / \(15^2=225\).

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Question 6/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

\(20^2 + 5\) का मान क्या है?

What is the value of \(20^2 + 5\)?

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Correct Answer

B. 405

Explanation

Simple Explanation

घात (exponent) पहले किया जाता है: \(20^2=400\)। फिर 5 जोड़ने पर \(400+5=405\) मिलता है। गलत विकल्पों की संभावित गलतियाँ: 395 संभवतः \(400-5\) करने की गलती से आता है; 415 तब आता है जब गलती से 15 जोड़ दिया गया हो; 420 संभवतः \(20\times21\) या कोई बहुगुणा समझकर मिलने वाला उत्तर है। परीक्षा टिप: घात पहले निकालें, फिर जोड़-घटाव करें और सामान्य अंकगणितीय ग़लतियों की जाँच करें। / Apply the exponent first: \(20^2=400\). Adding 5 gives \(400+5=405\). Why other choices are wrong: 395 likely comes from mistakenly subtracting 5 (\(400-5\)); 415 would arise if 15 were added instead of 5; 420 could come from confusing the expression with \(20\times21\). Exam tip: evaluate powers before addition and double-check simple arithmetic to avoid common slip-ups.

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Question 7/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

यदि \(c^3=343\) तो (c) क्या है?

If \(c^3=343\) then what is (c)?

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Correct Answer

C. 7

Explanation

Simple Explanation

\(7^3=343\)। / \(7^3=343\).

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Question 8/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

यदि \(d^2=324\) तो धनात्मक (d) क्या है?

If \(d^2=324\) then what is the positive value of (d)?

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Correct Answer

A. 18

Explanation

Simple Explanation

\(18^2=324\)। / \(18^2=324\).

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Question 9/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

यदि \(x^3=512\) तो (x) का मान क्या है?

If \(x^3=512\) then what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. 8

Explanation

Simple Explanation

\(8^3=512\)। घनमूल पहचानें। / \(8^3=512\). Recognize perfect cubes.

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Question 10/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

यदि \(y^2=441\) तो धनात्मक (y) क्या है?

If \(y^2=441\) then what is the positive value of (y)?

Explanation opens after your attempt

Correct Answer

A. 21

Explanation

Simple Explanation

\(21^2=441\)। वर्गमूल पहचानें। / \(21^2=441\). Recognize perfect squares.

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Question 11/11 Medium Mathematics Number Systems Exponents Class 9 Level 5

यदि \(z^3=729\) तो (z) का मान क्या है?

If \(z^3=729\) then what is the value of (z)?

Explanation opens after your attempt

Correct Answer

C. 9

Explanation

Simple Explanation

\(9^3=729\)। पूर्ण घनों को याद रखें। / \(9^3=729\). Remember perfect cubes.

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

यदि \(x^2=144\) तो धनात्मक (x) क्या है?

Simple Explanation

यदि \(a^3=216\) तो (a) क्या है?

Simple Explanation

निम्नलिखित का मान क्या है: \((17^2 - 8^2)\)?

Simple Explanation

182 + 192 का मान क्या है?

Simple Explanation

यदि \(b^2=225\) तो धनात्मक (b) क्या है?

Simple Explanation

\(20^2 + 5\) का मान क्या है?

Simple Explanation

यदि \(c^3=343\) तो (c) क्या है?

Simple Explanation

यदि \(d^2=324\) तो धनात्मक (d) क्या है?

Simple Explanation

यदि \(x^3=512\) तो (x) का मान क्या है?

Simple Explanation

यदि \(y^2=441\) तो धनात्मक (y) क्या है?

Simple Explanation

यदि \(z^3=729\) तो (z) का मान क्या है?

Simple Explanation

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18² + 19² का मान क्या है?