Using (√7 + √3)(√7 — √3) = 4 and the fact that (√7 + √3) is irrational prove that √7 — √3 is irrational.

Question

Philoid · Accepted Answer

Given ( + )( — ) = 4 and ( + ) is irrational.

(multiplying numerator and denominator by )

=

(we know that (a – b) × (a + b) = (a² – b²))

= =

Here, it is given that is irrational and we know that 4 is rational.

Therefore,

We know that rational divided by irrational is always irrational.

So, is irrational.