Question

How to simplify this?

Answer 1

`(6x^3y^3sqrt(15y))/sqrt(5xy)`

Explanation:

I am assuming the 3 before the radical in the numerator is not representing the 3rd root and the 12 is not a multiplier but a question number. If this is not the case then answer will be incorrect.

(1.) Factor the radicand in the numerator so you can extract roots.

`3sqrt(60x^6y^9)` can be factored as

`3sqrt(4* 15 *x^6 *y^8 *y)`

(2.) Extract roots. It can be seen for example that the root of `x^6` is `x^3`, since `x^3 * x^3 => x^6` and root of `y^8` is `y^4` since `y^4 * y^4 => y^8`.

`6x^3y^4sqrt(15y)`

(3.) Do the same with the denominator.

`sqrt(5xy^3) => sqrt(5 * x * y^2 * y) => ysqrt(5xy)`

`(6x^3y^4sqrt(15y))/(ysqrt(5xy)`

(4.) Cancelling like factors gives:

`(6x^3y^3sqrt(15y))/sqrt(5xy)`