square-root-3 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-3.
Which relation helps reach contradiction in the proof of \(\sqrt{3}\)?
B. \(a^2=3b^2\)
\(a^2=3b^2\) से (a) (3) से विभाज्य मिलता है। फिर (b) भी (3) से विभाज्य निकलता है। / From \(a^2=3b^2\), (a) becomes divisible by (3). Then (b) also becomes divisible by (3).
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What does assuming \(\sqrt{3}\) as \(\frac{a}{b}\) mean?
B. उसे परिमेय माननाAssuming it rational
किसी परिमेय संख्या को \(\frac{a}{b}\) रूप में लिखा जा सकता है। इसलिए यह परिमेय मान्यता है। / A rational number can be written in the form \(\frac{a}{b}\). So this is a rational assumption.
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Which statement about \(\sqrt{3}\) is correct?
B. \(\sqrt{3}\) अपरिमेय है\(\sqrt{3}\) is irrational
\(\sqrt{3}\) को परिमेय मानने से (a) और (b) दोनों (3) से विभाज्य निकलते हैं। यह विरोधाभास है। / Assuming \(\sqrt{3}\) rational makes both (a) and (b) divisible by (3). This is a contradiction.
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If \(\sqrt{3}=\frac{a}{b}\) and (a,b) are coprime then what is obtained by squaring?
A. \(a^2=3b^2\)
वर्ग करने पर \(3=\frac{a^2}{b^2}\) मिलता है। इससे \(a^2=3b^2\) बनता है। / Squaring gives \(3=\frac{a^2}{b^2}\). Hence \(a^2=3b^2\).
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What assumption is taken first to prove the irrationality of \(\sqrt{3}\)?
C. \(\sqrt{3}\) परिमेय है\(\sqrt{3}\) is rational
विरोधाभास के लिए पहले \(\sqrt{3}\) को परिमेय मानते हैं। फिर यह मान्यता गलत सिद्ध होती है। / For contradiction \(\sqrt{3}\) is first assumed rational. Then this assumption is shown false.
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