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Prove that Following Numbers Are Irrationals: 2 √ 7 - Mathematics

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Question

Prove that following numbers are irrationals:

\[\frac{2}{\sqrt{7}}\]
Numerical

Solution

(i) Let us assume that `2/sqrt7` is rational .Then , there exist positive co primes a and b such that

`2/sqrt7=a/b`

`sqrt7=(2b)/a`

`sqrt7`is rational number which is a contradication.

Hence `2/sqrt7` is irrational

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Chapter 1: Real Numbers - Exercise 1.5 [Page 49]

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RD Sharma Mathematics [English] Class 10
Chapter 1 Real Numbers
Exercise 1.5 | Q 2.1 | Page 49

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