(18) Simplify?

Question

lol i dont get these heres the link to the pic http://i52.photobucket.com/albums/g40/rivasamer/01-25-2007090129PM.jpg

Answer 1

5√(5/6) - 2√(6/5) + √120 =

Rationalize the denominators:

5√((5/6)(6/6)) - 2√((6/5)(5/5)) + √120 =

Factor perfect squares out of 120:

5√(30/36) - 2√(30/25) + √(4(30)) =

Split the radicals:

5√30/√36 - 2√30/√25 + √4√30 =

Simplify the perfect squares:

5√30/6 - 2√30/5 + 2√30 =

Factor out √30:

√30(5/6 - 2/5 + 2) =

Find a common denominator:

√30(25/30 - 12/30 + 60/30) =

73√30/30, choice C.