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

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Answer 1 · 2016-03-31T16:12:49

$+-sqrt(3x)/x$

Disregarding the possibilities of $+-$

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

Now view it as

$sqrt(16/4)= sqrt(4)=2$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 $+-sqrt(3x)/x$

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