How do you simplify #root3(150)*root3(20)#?
Dealing with roots is the same as dealing with exponents. Except the exponents for roots are fractions. Like this:
That means we can apply the distributive property of exponents to roots as well:
Now to our problem. If we factor both numbers we get that:
so our problem becomes:
Then we can combine both under one root, like so:
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:
or even better: