Question

Simplify:
(Ö 3 + Ö -7 )( Ö 3 - Ö -7 )

Answer 1

5xÖ72 + Ö8x²

Break 72 into prime factors

72 = 8·9 = 2·4·3·3 = 2·2·2·3·3

Break 8x² into prime factors

8x² = 2·4·x·x = 2·2·2·x·x

Substitute under radicals:
_________ _________
5xÖ2·2·2·3·3 + Ö2·2·2·x·x

Group like factors into pairs:
_____________ _____________
5xÖ(2·2)·2·(3·3) + Ö(2·2)·2·(x·x)

Write each pair as a square:
_______ _______
5xÖ2²·2·3² + Ö2²·2·x²