Question

prove underoot 7 is irrational number​

Answer 1

plzz refer to RD SHARMA class10

Answer 2

Solution :-

$let \: \sqrt{7} \: be \: rational$

and its simplest form be p/q.

$= > \sqrt{7} = p \div q$

On squaring both sides , we get :

=> 7 = p²/q²

=> p² = 7q²........(1)

p² is divisible by 7.

Therefore, p is also divisible by 7.

Let, p = 7r

On squaring both sides , we get:

p² = (7r)².......(2)

putting the value of p² in eqn 2 from 1

=> 7q² = 49r²

=>q² = 7r²

q² is divisible by 7

therefore, q is also divisible by 7.

Hence, p and q have common factors i.e. 7.

But our assumptions says that p and q have no common factor other than 1.

This is contradiction shows that our assumption is wrong.

Hence, proved .