SOLUTION: Please help and if possible try to explain 2/3 radical 14 multiplied by 12 radical 7 Thank you very much!

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Question 290171: Please help and if possible try to explain 2/3 radical 14 multiplied by 12 radical 7
Thank you very much!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2F3%29sqrt%2814%29%2A12sqrt%287%29
Since this is all multiplication and since multiplication is commutative and associative, we can reorder and rearrange this expression as we please:
%28%282%2F3%29%2A12%29%28sqrt%2814%29%2Asqrt%287%29%29
The first part is easy to multiply. For the square roots, we use the property of radicals: root%28a%2C+x%29%2Aroot%28a%2C+y%29+=+root%28a%2C+x%2Ay%29.
8sqrt%2898%29
And just like fractions should be reduced, if possible, square roots should be simplified. A square root can be simplified if its radicand has a perfect square factor. Since 98, the radicand, has 49 as a factor ans since 49 is a perfect square we can simplify sqrt%2898%29:
8sqrt%2849%2A2%29
Now we can use the earlier property, in reverse, to split this square root into two square roots:
8sqrt%2849%29%2Asqrt%282%29
And since sqrt%2849%29+=+7:
8%2A7%2Asqrt%282%29
which simplifies to:
56sqrt%282%29