prove that 5 root 2 is an irrational number given that root 2 is an irrational number

Dear Student

Let us assume 5√2 to be Rational
Then,
5√2 = a / b [ Where, a & b are co-prime and b ≠ 0 ]

√2 = a / 5b

a / 5b is rational

But, we know √2 is Irrational

This contradiction arise due to our wrong supposition that 5√2 is Rational.

Hence,
5√2 is Irrational ! ! !

​​​Regards