Help with radicals?

Question

I need some help with a few of these problems.

Simplify:

√75/162
√3/7
2√21 x √ 35

Answer 1

Here's what you do to simplify radicals. You try to factor out the squared number(s) in the radical (usually i do this under the radical first), then put the square root of that number outside the radical. Remember that you can multiply radicals together, but only when a radical is multiplied against itself does it become a non-radical number (example: √7 * √7 = √49 = 7).

So:
√75/162 = √(25*3)/(81*2) = √((5^2)*3)/((9^2)*2) = 5/9√3/2
√3/7 cannot be simplified; neither numerator nor denominator contains a squared factor
2√21 * √35 = √4*3*7 * √5*7 = √4*√*3*√5*7 = 7√60 = 7√15*4 = 14√15

Answer 2

√75/162 = √(3*25) / 162 = (5√3)/162

√3/7 = √3/7 there is nothing to simplify

2√21 x √ 35 = 2√(21*35) = 2√(3*7*5*7) = 2*7√(3*5) = 14√15