Question

Prove (√5-√3)² as irrational

Answer 1

Answer:

$(\sqrt{5} - \sqrt{3} )^{2}\\ =5 - 3 -2\sqrt{15}\\ = 2-2\sqrt{15}\\ =2(1-\sqrt{15})$

now 1 - sqrt(15) is irrational

and if we multiply a rational number and an irrational number the result is rational thus (√5-√3)² is an irrational number