SOLUTION: Tutor, Good Evening. I am not understanding square roots at all for some reason. Could you please help me by explaining these two problems? Perform the indicated division.

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Question 100430: Tutor,
Good Evening. I am not understanding square roots at all for some reason. Could you please help me by explaining these two problems?
Perform the indicated division. Rationalize the denominator if necessary. Then simplify each radical expression.
1.) 18 + sqrt 567 / 9
2.) -9 - sqrt 108 / 3
I do not understand these problems at all so any help is appreciated. Thank you very much for your time and help.
Found 2 solutions by checkley71, edjones:
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
1) 18+sqrt(567/9) divide 567 by 9=63
18+sqrt(63) now find the factors of 63=9*7
18+sqrt(9*7) now extract the sqrt of 9=3
18+3sqrt7 now combine the terms by fatcoring out 3
3(6+sqrt7) answer.
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2) -9-sqrt(108/3) again divide 108 by 3=36
-9sqrt36=-9*6=-54 answer.
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Always look for ways to simplify these type of problems.
They always look more difficult than they actually are.

Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
if the number in the sqrt box isn't a square maybe one of its factors is a square and it can come out.
18 + sqrt 567 / 9
18+sqrt(3*3*3*3*7)/9=18+9sqrt(7)/9=18+sqrt(7)
.
-9-sqrt(4*3*3*3)/3=-9-6sqrt(3)/3=-9-2sqrt(3)
hope that helps.
Ed