Question

How do you simplify `sqrt(320y^2)`?

Answer 1

`sqrt(320y^2) = 8sqrt(5)abs(y)`

Explanation:

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

In our example, we know that `y^2 = abs(y)^2 >= 0`

In addition note that `320 = 64*5 = 8^2*5`

So:

`sqrt(320y^2) = sqrt(8^2*5*abs(y)^2) = sqrt(8^2)*sqrt(5)*sqrt(abs(y)^2) = 8sqrt(5)abs(y)`