SOLUTION: what is the solution to 3 square root 75 + 9 square root 108?

Question 413843: what is the solution to 3 square root 75 + 9 square root 108?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Like radical terms have the same kind(s) of roots with the same radicands. (The expression inside a radical is called a radicand.) Both of these terms have the same kind of root, square roots, but their radicands are different, 75 and 108. So we cannot add them together. Only like terms can be added.

But radical expressions can sometimes be simplified so we can try to simplify the square roots. Simplifying square roots involves finding perfect square factors (other than 1) of the radicands. Both of your radicands have perfect square factors so they will simplify:

Now we use a property of radicals, , to split the square root so the each factor is in its own square root:

The square roots of the perfect squares simplify:

which simplifies to:

Not only did the square roots simplify but we now have like terms (two square roots with radicands of 3)! So unlike earlier, we can now add them together. Exactly like 15x + 54x = 69x:

BTW: The word "solution" applies to equations and inequalities. This problem was an expression. Expressions are "simplified".
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