How do you simplify $root3(150)*root3(20)$ ?

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Answer 1 · 2016-10-21T11:56:41

$10root(3)3$

Dealing with roots is the same as dealing with exponents. Except the exponents for roots are fractions. Like this:
$root(3)x=x^(1/3)$

That means we can apply the distributive property of exponents to roots as well:
$root(3)(x*y)=(x*y)^(1/3)=x^(1/3)*y^(1/3)$

Now to our problem. If we factor both numbers we get that:
$150=5*5*3*2$
$20=5*2*2$

so our problem becomes:
$root(3)(5*5*3*2)*root(3)(5*2*2)$

Then we can combine both under one root, like so:
$root(3)(5*5*3*2*5*2*2)$

As you can see there are three 5s and three 2s in there, meaning we can take them to the outside of the root like this:
$5*2root(3)3$

or even better:
$10root(3)3$

How do you simplify root3(150)*root3(20)root3(150)*root3(20)?