Question

Rationalise the denominator: 1÷√7+√3-√2

Answer 1

1/(√7+√3-√2)

multiply numerator and denominator by (√7+√3+√2)

=(√7+√3+√2)/[(√7+√3)-(√2)][(√7+√3)+(√2)]

=(√7+√3+√2)/(√7+√3)²-(√2)²

=(√7+√3+√2)/(√7)²+(√3)²+2(√7)(√3)-2

=(√7+√3+√2)/7+3+2(√21)-2

=(√7+√3+√2)/8+2(√21)

multiply numerator and denominator by 8–2(√21)

(√7+√3+√2)[8–2(√21)]/[8+2(√21)][8–2(√21)]

=(√7+√3+√2)[8–2(√21)]/[8]²-[2(√21)]²

=(√7+√3+√2)[8–2(√21)]/64–4*21

=(√7+√3+√2)[8–2(√21)]/64–84

=-(√7+√3+√2)[8–2(√21)]/20