Question

How do you rationalize the denominator and simplify `sqrt(9xy)/(sqrt(3x^2y)`?

Answer 1

`+-sqrt(3x)/x`

Explanation:

Disregarding the possibilities of `+-`

Consider the example
`sqrt(16)/(sqrt(4))=4/2=2`

Now view it as

`sqrt(16/4)= sqrt(4)=2`
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Given: `sqrt(9xy)/sqrt(3x^2y)`

Write as

`sqrt( (9xy)/(3x^2y))" "=" "sqrt( 3/x)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is format is frowned upon so we need to 'get rid' of the root in the denominator.

Multiply by 1 but in the form of `1=sqrt(x)/sqrt(x)`

`sqrt(3)/sqrt(x)xxsqrt(x)/(sqrt(x)) = sqrt(3x)/x`

Now think about `(-2)xx(-2)=+4=(+2)xx(+2)`

So our answer needs to be `+-sqrt(3x)/x`