Question

1. Prove that
$\sqrt{7} \: is \: irrationl.$
Standard:- 10

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Answer 1

Hey Mate

your answer is --

Let, us assume on contrary that √7 is rational .

so, √7 = a/b where a and b are integer and b ≠ 0.
Let, a and b are co - prime

taking square on both side

=> 7 = a^2/b^2

=> 7b^2 = a^2 .....(1)

=> a^2/7

=> a/7

taking some constant c

a = 7c

squaring both side

a^2 = 49c^2

=> 7b^2 = 49c^2 { from 1 }

=> b^2 = 7c^2

=> b^2/7

=> b/7

so, a and b have at least 7 as a common prime factor

but, this contradict the fact that a and b are co - prime .

therefore , our assumption is wrong

✔hence, √7 is irrational

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