SOLUTION: 7 √32 / 9 √8

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Question 343532: 7 √32 / 9 √8
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
7sqrt%2832%29%2F9sqrt%288%29
As is often the case in Math, there is more than one way to simplify this expression. To me the easiest way is based on noticing that dividing 32 and 8 (which are currently inside separate square roots) results in 4 which is a prefect square!

So we will start by getting the 32 and the 8 into the same square root. First we'll use basic Algebra to split this fraction in two:
%287%2F9%29%2A%28sqrt%2832%29%2Fsqrt%288%29%29
Now we can use one of the properties of radicals:
sqrt%28a%29%2Fsqrt%28b%29+=+sqrt%28a%2Fb%29
to combine the square roots of the second fraction into a single square root:
%287%2F9%29%2Asqrt%2832%2F8%29
Now we can replace the 32/8 with a 4:
%287%2F9%29%2Asqrt%284%29
and the sqrt%284%29 with a 2:
%287%2F9%29%2A2
And we finish by multiplying:
14%2F9
(I'll leave it up to you to change this improper fraction into a mixed number.)