Question

show that 5√2is an irrational number​

Answer 1

Let 5√2 be a rational number .

So, it is of the form p/q , where p and q are co - primes ( not having any factor other than 1 ) and q is not equal to 0.

Then , 5√2 = p/q.

√2 = p/q ÷ 5.

√2 = p/5q.

So, it contradicts the fact that √2 is irrational.

Thus , our assumption is wrong. i.e. 5√2 is rational.

So, 5√2 is irrational.

Hence proved.