Question

state whether the number (root 2-root 3) (root 2 +root 3) is rational or irrational justify

Answer 1

(root 2 - root3)(root2 +root3)

=root2^2-root3^2
=2-3
= -1

Answer 2

Using (a - b)(a + b) = a2 - b2, we have

(√2 - √3)(√2 + √3) = (√2)2 - (√3)2 = 2 - 3 = -1

Since -1 can be expressed in the p/q form as -1/1, (√2 - √3)(√2 + √3) is rational