Question

How do you simplify `(5+ sqrt 5)/(8- sqrt 5)`?

Answer 1

By multiply numerator and denominator by denominator's conjugate pair. Solution is `(45+13√5)/(59)`

Explanation:

To simplify `(5+√5)/(8−√5)`, one has to multiply numerator and denominator by denominator's conjugate pair which is `(8+√5)`.

Hence, `(5+√5)/(8−√5)` becomes

`((5+√5)(8+√5))/((8−√5)(8+√5))` i.e.

`(40+5√5+8√5+5)/(64−5)` i.e.

`(45+13√5)/(59)`