Question

How do you simplify `1/3sqrt252`?

Answer 1

`1/3 sqrt(252) = 2 sqrt(7)`

Explanation:

If `a, b >= 0` then `sqrt(ab) = sqrt(a)sqrt(b)`

`252 = 2^2*3^2*7`

So:

`1/3 sqrt(252) = 1/3 sqrt(2^2 * 3^2 * 7) = 1/3 sqrt(2^2 * 3^2) sqrt(7)`

`= 1/3 sqrt((2 * 3)^2) sqrt(7) = 1/3*2*3*sqrt(7) = 2sqrt(7)`