You can put this solution on YOUR website! I assume the problem is to simplify these square roots. Simplifying square roots is kind of like reducing fractions. Not all fractions can be reduced and not all square roots can be simplified. When we can reduce a fraction we either end up with an equivalent whole number or an equivalent fraction written with smaller "simpler" numbers. When we simplify a square root we either end up with an equivalent whole number or an equivalent square root written with smaller "simpler" numbers.
The way to simplify square roots is factor out perfect square factors (other than 1), if any. If we can find perfect square factors we can then "separate" them into separate square roots which can then be simplified separately. The property which allows us to separate square roots this way is: .
Let's see how this works on your problems:
Find perfect square factors. 9 is a perfect square and it is a factor of 18:
Separate the square roots:
Simplify the square root of the perfect square:
And finally, just like reducing fractions, repeat the process until you can't go any further. Burt since there is no perfect square factor of 2 (other than 1), there is no more we can do.
Using the Commutative Property of Multiplication we can reorder the multiplication:
Then we can combine the two square roots, using the property above in reverse:
If we're clever, we can avoid this last step by using the Commutative Property inside the square root and by keeping the non-perfect square factors together:
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