Question

How do you simplify `sqrt(108x^3y^5 )`?

Answer 1

`6xy^2sqrt(3y)`

Explanation:

We are looking for values that are squared. These can be taken outside the square root in non-squared form.

Using a factor tree to deal with the number 108

So the prime factors are: `2^2xx3^2xx3`

`x^3` is the same as: `x^2xx x`
`y^5` is the same as: `y^2xxy^2xxy`

Thus write: `sqrt(108x^3y^5)` as `sqrt(2^2xx3^3xx3xx x^2xx x xxy^2xxy^2xxy)`

Taking the squared values outside the root gives:

`2xx3xx x xxy^2xxsqrt(3xy)`

`6xy^2sqrt(3xy)`