SOLUTION: what is the answer to {{{sqrt(6)*sqrt(66)}}}

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Question 205245This question is from textbook
: what is the answer to sqrt%286%29%2Asqrt%2866%29 This question is from textbook

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
There is an important property of square roots which we can use to multiply them:
sqrt%28a%29%2Asqrt%28b%29+=+sqrt%28a%2Ab%29
So your problem becomes:
sqrt%286%29%2Asqrt%2866%29+=+sqrt%286%2A66%29
The only thing we can do now is to simplify the square root as much as possible. To simplify square roots we look for perfect square factors. If we factor 66 we will see a perfect square factor:
sqrt%286%2A66%29+=+sqrt%286%2A6%2A11%29+=+sqrt%286%5E2%2A11%29
Now we can use the property as above, in reverse, to split the perfect square factor for the other factor:
sqrt%286%5E2%2A11%29+=+sqrt%286%5E2%29%2Asqrt%2811%29+=+6sqrt%2811%29