Question

Rationalise the denominator of 15/√6+√5-√11

Answer 1

15/( √5 + √6 -√11 )

= 15( √5 + √6 + √11)/( √5 + √6 -√11)(√5 + √6 + √11)

= 15( √5 + √6 + √11)/{ (√5 + √6)² - √11²}

= 15( √5 + √6 + √11)/{ 11+2√30 -11}

= 15( √5 + √6 + √11)/2√30

again,

= 15(√5 + √6 + √11)√30/(2√30)(√30)

= 15(√150 + √180 + √330 )/60

= ( √150 + √180 + √330)/4

Answer 2

15/(√5 + √6 -√11)

= 15(√5 + √6 + √11)/(√5 + √6 -√11)(√5 + √6 + √11)

= 15(√5 + √6 + √11)/{(√5 + √6)² - √11²}

= 15(√5 + √6 + √11)/{√5²+√6²+2(√5)(√6) - 11}

= 15(√5+√6+√11)/(5+6+2√30 - 11)

= 15(√5 + √6 + √11)/{ 11+2√30 -11}

= 15( √5 + √6 + √11)/2√30

Again we have to rationalise,

= 15(√5 + √6 + √11)×√30/(2√30)(√30)

= 15(√150 + √180 + √330)/60

= (√150 + √180 + √330)/4

Now the denominator is rationlised.

Hope it helps