Question

How do you simplify `sqrt(108x^5y^8)`?

Answer 1

`6x^2y^4sqrt(3x)`

Explanation:

We can think of `sqrt(108x^5y^8` as the same as `sqrt(108 xx x^5 xx y^8`. Then we can can square root each number individually to get `6x^2y^4sqrt(3x)`

So the square root of 108 is `6sqrt(3)` because `sqrt108` can also be written as `sqrt(36 xx 3)`. We know the square root of 36 to be 6, so we write 6 outside of the square root. Thus we have `6sqrt(3)` so far.

Then we can do the same for `x^5 xx y^8`. However, when square rooting powers, we divide the power by the root. For example `sqrt(y^8)` becomes `y^4`. For `sqrt(x^5)`, we get `x^2sqrt(x)` because we can only square root 4 so we have a remainder.

We can then put all of these answers together to get `6x^2y^4sqrt(3x)`

Answer 2

`6x^2y^4sqrt(3)`

Explanation:

Looking for squared values we have:

`sqrt(6^2xx3xx x^2xx x^2xx x xxy^2xxy^2xxy^2xxy^2)`

`6x^2y^4sqrt(3)`

Have a look at: https://socratic.org/s/aCtLpnUs