Question

How do I solve 8+√ 2 / 8-√ 2 ?
I know I need to change the denominator to a positive use the foil method on both the numerator and denominator but then I get confused from there. Or if I need to do it a different way please let me know.

Answer 1

8+√ 2 / 8-√ 2

= (8+√ 2 / 8-√ 2) × (8+√ 2 / 8+√ 2)

= (8+2√2)² / {8²-(2√2)²}

= {8²+2.8.2√2 +(2√2)²} / (64-2×2)

= (64+32√2+2×2)/(64-4)

= (64+32√2+4)/60

= (68+32√2)/60

= {4(17+8√2)} /60

= (17+8√2)/15 Answer