Question

How do you simplify `(5sqrt15) /( 3sqrt27)`?

Answer 1

Same thing. Just a very slightly different presentation!

`(5sqrt(5))/9`

Explanation:

The answer given was stopped at `(5sqrt(5))/(3sqrt(9))`

`color(red)("'~~~~~~~~~~~~~~~~ Something to think about! ~~~~~~~~~~~")`

It is considered better mathematical practice if you 'get rid' of any roots that are in the denominator (bottom number)

The method is based on: Multiply any number by 1 and you do not change its inherent value

So `(5sqrt(5))/(3sqrt(9))xx1` does not change its value

Suppose we wrote 1 as `(sqrt(9))/(sqrt(9))`

This is still 1

`color(red)("'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")`
`color(blue)("Back to solving the question")`

Multiply by 1 but in the form of `(sqrt(9))/(sqrt(9))` giving

`(5sqrt(5))/(3sqrt(9))xx(sqrt(9))/(sqrt(9))" "=" "(5sqrt(5)sqrt(9))/(3sqrt(9)sqrt(9))`

`(5sqrt(5)sqrt(9))/(3xx9)`

But `sqrt(9)=3` giving:

`(5xx3xxsqrt(5))/(3xx9)" "=" " 3/3xx(5sqrt(5))/9`

But `3/3=1` giving:

`(5sqrt(5))/9`