Question

Express 3/root 3-root 2 + root 5 with rational denominator ​

Answer 1

Ans

First we have to rationalize the denominator:

3 / (√3-√2) -√5* (√3-√2)-√5 / (√3-√2)-√5

=3(√3-√2-√5) / (√3-√2)^2 - (√5)^2

=3(√3-√2-√5) / [(√3)^2+(√2)^2- 2*√3*√2] -5. (Solve (√3-√2)^2 using

a+b whole square formulae)

= 3(√3-√2-√5) / (3+2-2√6) -5

= 3(√3-√2-√5)/ -2√6

Again rationalize the denominator:

3(√3-√2-√5) / -2√6. * √6/√6

=3(√18-√12-√30)/ -12

=3(3√3-2√3-√30)/ -12

=( 3√2-2√3-√30 )/ -4

This is the answer: ⬆.

Hope it helped..