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decimal-approximation MCQ Questions for Class 10

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3 questions tagged with decimal-approximation.

Question 1/3 Hard Mathematics Polynomials Representing real numbers on the number line Class 10 Level 49

यदि (A) संख्या रेखा पर (1.4) और (1.5) के बीच है और \(A=\sqrt{2}\) है, तो सबसे सही कथन कौन-सा है?

If (A) lies between (1.4) and (1.5) on the number line and \(A=\sqrt{2}\), which statement is most correct?

Explanation opens after your attempt
Correct Answer

A. \(1.4<\sqrt{2}<1.5\)

Step 1

Concept

Because \(1.4^2=1.96\) and \(1.5^2=2.25\), \(\sqrt{2}\) lies between them. For hard questions, use squares of decimals.

Step 2

Why this answer is correct

The correct answer is A. \(1.4<\sqrt{2}<1.5\). Because \(1.4^2=1.96\) and \(1.5^2=2.25\), \(\sqrt{2}\) lies between them. For hard questions, use squares of decimals.

Step 3

Exam Tip

क्योंकि \(1.4^2=1.96\) और \(1.5^2=2.25\), इसलिए \(\sqrt{2}\) इनके बीच है। कठिन प्रश्नों में दशमलव के वर्ग का प्रयोग करें।

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Question 2/3 Expert Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 18

यदि कोई छात्र \(\sqrt{3}\approx1.732\) लिखकर उसे अपरिमेय सिद्ध मान लेता है, तो मुख्य कमी क्या है?

If a student writes \(\sqrt{3}\approx1.732\) and treats it as proof of irrationality, what is the main weakness?

Explanation opens after your attempt
Correct Answer

A. दशमलव अनुमान पूर्ण प्रमाण नहीं होताA decimal approximation is not a complete proof

Step 1

Concept

(1.732) is only an approximate value, not the full value.

Step 2

Why this answer is correct

To prove irrationality, we must assume rationality and show a contradiction with coprimality.

Step 3

Exam Tip

In exams, write a logical proof, not an approximation. चरण 1: (1.732) केवल निकट मान है, पूरा मान नहीं। चरण 2: अपरिमेयता सिद्ध करने के लिए परिमेय मानकर सहअभाज्यता का विरोधाभास दिखाना पड़ता है। चरण 3: परीक्षा में अनुमान नहीं, तार्किक प्रमाण लिखें।

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Question 3/3 Expert Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 17

यदि कोई छात्र \(\sqrt{5}\) को परिमेय सिद्ध करने के लिए केवल \(\sqrt{5}\approx2.236\) लिखता है, तो यह तर्क क्यों अधूरा है?

If a student writes only \(\sqrt{5}\approx2.236\) to prove rationality or irrationality, why is this argument incomplete?

Explanation opens after your attempt
Correct Answer

A. दशमलव का सीमित अनुमान प्रमाण नहीं होताA finite decimal approximation is not a proof

Step 1

Concept

(2.236) is only an approximate value, not the full value.

Step 2

Why this answer is correct

To prove irrationality, we must assume rationality and show a contradiction.

Step 3

Exam Tip

In exams, do not write a decimal approximation in place of proof. चरण 1: (2.236) केवल अनुमानित मान है, पूरा मान नहीं। चरण 2: अपरिमेयता सिद्ध करने के लिए परिमेय मानकर विरोधाभास दिखाना पड़ता है। चरण 3: परीक्षा में दशमलव अनुमान को प्रमाण की जगह न लिखें।

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