Question

Can you combine `y^ { 2} \sqrt { 3y ^ { 2} } - 4v \sqrt { 48y ^ { 5} }`? If so, how?

Answer 1

No, you can't combine. You can simplify, though.

Explanation:

First, we observe that `48 = 16 * 3`. Hence, the radical becomes

`y^2sqrt(3y^2) - 4vsqrt(16 * 3 * y^5)`

`y^2sqrt(3y^2) - 4v(4)sqrt(3y^5)`

`y^2sqrt(3y^2) - 16vsqrt(3y^5)`

Now consider the variables. We have that `sqrt(y^2) = (y^2)^(1/2) = y`. Hence,

`y^2(y)sqrt(3) - 16vsqrt(3(y^2)^2y)`

`y^3sqrt(3) - 16vy^2sqrt(3y)`

Since `sqrt(3)` and `sqrt(3y)` aren't like terms, we cannot combine them, and this is as far as we can go.

Hopefully this helps!