Radicals question?

Question

Hi,
Can you please explain how to do this?
Change to entire radicals:
2root3
11root2

Thanks,

Answer 1

2√3
This is simply:
2 * √3

And 2 is the same as √2 * √2
= √2 * √2 * √3

The product of square roots is the same as the square root of the product:
= √(2 * 2 * 3)

= √12

Similarly for 11√2

= √11 * √11 * √2
= √(11 * 11 * 2)

= √242

Once you've done it the long way, you can use a short cut: If you had a√b, you would square a and put it inside the √ symbol.

2√3 = sqrt(2² * 3) = sqrt(4 * 3) = sqrt(12)
11√2 = sqrt(11² * 2) = sqrt(121 * 2) = sqrt(242)

Answer 2

2rt3 = rt(2x2x3) = rt12, and

11rt2 = rt(11x11x2) = rt242