Question 374550
{{{sqrt(75p^3q^4)}}}
When there are no fractions, like in this expression, all there is to simplifying square roots is to "remove" any perfect square factors of the radicand (the expression inside a radical is called the radicand). This radicand has several perfect square factors:
{{{sqrt(25*3*p^2*p*(q^2)^2*q)}}}
I find it helps to use the Commutative Property to rearrange the order so that the perfect square factors are together (in front):
{{{sqrt(25*p^2*(q^2)^2*3*p*q)}}}
Now we use a property of radicals, {{{root(a, x*y) = root(a, x)*root(a, y)}}}, to separate all the perfect square factors into their own square roots:
{{{sqrt(25)*sqrt(p^2)*sqrt((q^2)^2)*sqrt(3*p*q)}}}
Each of the square roots with a perfect square radicand can be simplified:
{{{5*p*q^2*sqrt(3pq)}}}