square-root-2 se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
5 questions tagged with square-root-2.
Which relation helps reach contradiction in the proof of \(\sqrt{2}\)?
A. \(p^2=2q^2\)
\(p^2=2q^2\) से (p) सम मिलता है। फिर (q) भी सम निकलता है और विरोधाभास बनता है। / From \(p^2=2q^2\), (p) becomes even. Then (q) also becomes even and a contradiction is formed.
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What does assuming \(\sqrt{2}\) as \(\frac{p}{q}\) mean?
A. उसे परिमेय माननाAssuming it rational
परिमेय संख्या को दो पूर्णांकों के अनुपात के रूप में लिखा जा सकता है। इसलिए \(\sqrt{2}=\frac{p}{q}\) मानना उसे परिमेय मानना है। / A rational number can be written as a ratio of two integers. So assuming \(\sqrt{2}=\frac{p}{q}\) means assuming it rational.
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Which statement about \(\sqrt{2}\) is correct?
A. \(\sqrt{2}\) अपरिमेय है\(\sqrt{2}\) is irrational
\(\sqrt{2}\) को परिमेय मानने पर विरोधाभास मिलता है। इसलिए यह अपरिमेय है। / Assuming \(\sqrt{2}\) rational gives a contradiction. Therefore it is irrational.
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Which relation is obtained by squaring \(\sqrt{2}=\frac{p}{q}\)?
C. \(p^2=2q^2\)
वर्ग करने पर \(2=\frac{p^2}{q^2}\) मिलता है। इससे \(p^2=2q^2\) बनता है। / Squaring gives \(2=\frac{p^2}{q^2}\). Hence \(p^2=2q^2\).
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What assumption is taken first to prove the irrationality of \(\sqrt{2}\)?
A. \(\sqrt{2}\) परिमेय है\(\sqrt{2}\) is rational
विरोधाभास विधि में पहले \(\sqrt{2}\) को परिमेय मानते हैं। फिर इसी मान्यता से विरोधाभास निकाला जाता है। / In contradiction method we first assume \(\sqrt{2}\) is rational. Then a contradiction is obtained from this assumption.
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