Question

How do you simplify square root of 4y^3 - square root y^3?

Answer 1

`sqrt(4y^3) - sqrt(y^3)= y sqrt(y)`

Explanation:

The useful rule for square roots here is that `sqrt(ab) = sqrt(a)sqrt(b)`

This means that `sqrt(4y^3) = sqrt(4y^2y) = sqrt(4) sqrt(y^2) sqrt(y)`, which can be simplified to `2 y sqrt(y)`

`sqrt(y^3)` is similarly simplified to `sqrt(y^2y) = sqrt(y^2) sqrt(y) = ysqrt(y)`.

Subtracting the second from the first gives us
`2 y sqrt(y) - ysqrt(y) = ysqrt(y)`