Question

answer q no. 8 please​

Answer 1

Let's solve this by indirect proof,,,

Let's assume that √7-3 is a Rational Number.

So it can be written in p/q form ,

hence,

√7-3=p/q

√7 q =p+3q

here (p,q) are integers ,

LHS=Irrational

RHS=Rational

so,

LHS≠RHS

This is a contradiction,

Hence our assumption is wrong,

Hence √7-3 is an irrational number.

Hope it helps

Answer 2

Let us assume that √7 - 3 is rational.Then it will be of the form a/b ,where a,b are coprime Integers and b≠0.

√7 - 3 = a/b

On rearranging ,

√7= a/b + 3

Since,a/b and 3 are rational. So their sum will be rational.

Therefore √7 is rational number.

But we know that, √7 is irrational number.

Thus , there is a contradiction. Hence Our assumption is wrong that √7 - 3 is rational.

Hence,√7 - 3 is irrational

HOPE THIS WILL HELP YOU