Question

Rationalize the denominator of 1/√2+√3+√5

Answer 1

Hi friend!!

1/(√2+√3+√5)

→ 1/(√2+√3+√5) × (√2+√3-√5)/(√2+√3-√5)

→ (√2+√3-√5)/(√2+√3+√5)(√2+√3-√5)

→ (√2+√3-√5)/{(√2+√3)²-(√5)²}

→ (√2+√3-√5)/{√2²+√3²+2(√2)(√3) - 5}

→ (√2+√3-√5)/{2+3+2√6 - 5}

→ (√2+√3-√5)/2√6

The denominator is still irrational.

So we have to rationalise it further.

→ (√2+√3-√5)/2√6 × √6/√6

→ √6(√2+√3-√5)/2(√6)²

→ √12+√18-√30/2(6)

→ √4×3 + √9×2 - √30/12

→ (2√3+3√2-√30)/12

Hope it helps...