SOLUTION: Express the radical in simplified form. Assume all variables represent positive real numbers. square root of ((72a^4)(b^3))

Question 274469: Express the radical in simplified form. Assume all variables represent positive real numbers.
square root of ((72a^4)(b^3))
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Simplifying square roots is just a matter of

Since you have no denominators we only have to deal with the first item: Finding perfect square factors, if any. There are several:

Now we use a property of radicals, to separate all the perfect square factors into their own square roots:

We can now simplify the square roots of the perfect squares:

Since this is all multiplication we can use the Commutative Property to rearrange the factors. We'll put the square roots in the back:

And last of all we can use the same property as before but this time we'll use it to combine the remaining square roots:

This is the simplified form of your original expression.
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