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

Feb 16, 2016

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)