Question

Prove that √5-√7 is an irrational number

Answer 1

It is a rational no. if it can be represented in the form p/q where p and q are co primes and q is non-zero.

So,√5-√7=p/q

:- √5 = p/q + √7/1

:- √5 = (p+q√7)/q

Both LHS and RHS are irrational i.e. non terminating and non reccuring decimals.

I hope this would help you