Question

√200a^6

Answer 1

10a^3sqrt2

Answer 2

Square roots is all about taking out doubles.
sqrt(4) can be rewritten as sqrt(2*2).
There are two twos, so you can take a two out.
sqrt(4) = 2

sqrt(200a^6) can be broken up by doing:
sqrt(2*100 * a^3 * a^3)
sqrt(2*2*50 * a^3 * a^3)
sqrt(2*2*5*5*2 * a^3 * a^3)
We have one pair of twos, one pair of fives, and one pair of a cubeds. Taking that out, we get:

2*5*a^3 * sqrt(2)

Simplifying, we find the answer:
10a³sqrt(2)