SOLUTION: I need help simplying radicals by factoring.

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Question 171500This question is from textbook
: I need help simplying radicals by factoring. This question is from textbook

Answer by solver91311(6137) About Me  (Show Source):
You can put this solution on YOUR website!
Share a problem and someone will try to help you. In general, if you are factoring the expression under a radical, look for factors that are perfect squares.

For example, if you are faced with sqrt%28c%29, but you know that c=a%5E2b, then you can write sqrt%28c%29=sqrt%28a%5E2b%29=a%2Asqrt%28b%29

For a specific example, simplify sqrt%2812%29. We know that 12=4%2A3, but since 4=2%5E2, 12+=+2%5E2%2A3, so sqrt%2812%29=sqrt%282%5E2%2A3%29=2%2Asqrt%283%29

For a more complex specific example, consider sqrt%28r%5E2%2As%2B2rs%2Bs%29

Factor r%5E2%2As%2B2rs%2Bs completely: s%28r%2B1%29%28r%2B1%29=s%28r%2B1%29%5E2. Now we have:

sqrt%28r%5E2%2As%2B2rs%2Bs%29=sqrt%28s%28r%2B1%29%5E2%29 which can be written %28r%2B1%29sqrt%28s%29