Radicals Radicals Radicals?

Question

I know theres a name for this type of problem but i cant put my finger on how to do it

2 + square root of 5

3 - square root of 7

^^ That is a fraction

Answer 1

2 + square root of 5/ 3 - square root of 7

= (2 + square root of 5)/ (3 - square root of 7)

= (2 + √5)/ (3 - √ 7)

it is called rationalise the denominators. ie. multiply and divide by conjugate of denominator.I hope you understand the meaning.

conjugate of (3 – √7) is ( 3 + √7)

(2 + √5)/ (3 - √ 7)

=  (2 + √5)(3 + √7)/ (3 - √ 7) (3 + √7)

=  (6 + 3√5+ 2√7 + √35)/ (9 –  7)

=  (6 + 3√5+ 2√7 + √35)/ 2

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