Rationalize the denominator and simplify.

Question

Rationalize the denominator and simplify.

 

√30

_______

6√5+5√6

Answer 1

Natalie, I hope I can still help!

 

We first have to multiply the numerator and denominator by (6√5 - 5√6). 

 

√30(6√5 - 5√6) = 6√150 = 5√180 = 5√(36(5)) = 5(6)√5 = 30√5

 

(6√5+5√6)(6√5 - 5√6) = 36(5) + 30√30 - 30√30 - 25(6) = 180 - 150 = 30

 

The final answer is 30√5/30 = √5