Question

rationalise
1/(√2+√3-√5)

Answer 1

1/(√2+√3-√5)

Rationalising factor = √2+√3+√5

1/(√2+√3-√5)×(√2+√3+√5)/(√2+√3+√5)

→ √2+√3+√5/[(√2+√3)² - (√5²)]

→ √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.

Now,rationalising factor = √6

→ √2+√3+√5/2√6 ×√6/√6

→ √6(√2+√3+√5)/2(√6)²

→ √12+√18+√30/2(6)

→ √12+√18+√30/12

→ (2√3+3√2+√30)/12

It is rationalised now.

Hope it helps