Question

Prove root m is irrational

Answer 1

Prove root m is irrational

√M + √N is an irrational number. Now, √MN which is an irrational number as M and N are primes is equal to a Rational number where ( p ≠ 0, q ≠ 0, M ≠ 0, N ≠ 0 ) is a contradiction. ... Hence, √M + √N is an irrational number [ proof by contradiction ].

Prove root n is irrational

If n is a perfect square then √n is a an integer and therefore rational, so it suffices to prove that if n is not a perfect square, then √n is irrational.

Answer 2

Answer:

Answer. √M + √N is an irrational number. ... If n is a perfect square then √n is a an integer and therefore rational, so it suffices to prove that if n is not a perfect square, then √n is irrational