Question 383712
{{{sqrt(16/(9xy^2))}}}
As often happens in Math, there are sever ways to do this. The way I like to do it is:
1. Make the denominator a perfect square.
9 is a perfect square and so is {{{y^2}}}. Only the x in the denominator is not a perfect square. To make the denominator a perfect square, then, we just have to change x into {{{x^2}}} somehow. This can be done by simply multiplying the numerator and denominator of the fraction by x:
{{{sqrt((16/(9xy^2))(x/x))}}}
which gives us:
{{{sqrt((16x)/(9x^2y^2))}}}
Now we can use a property of radicals, {{{root(a, p/q) = root(a, p)/root(a, q)}}}, to separate the numerator and denominator into separate square roots:
{{{sqrt(16x)/sqrt(9x^2y^2)}}}
The denominator, being the square root of a perfect square, simplifies easily:
{{{sqrt(16x)/3xy}}}
The numerator has a perfect square factor, 16. So we can simplify that, too.
Using another property of radicals, {{{root(a, p*q) = root(a, p)*root(a, q)}}}, we can separate the factors into their own square roots:
{{{(sqrt(16)sqrt(x))/3xy}}}
And the square root of 16 is 4:
{{{(4sqrt(x))/3xy}}}
This is a simplified expression with a rational denominator.