SOLUTION: Multiply and simplify. Assume that all variables represent nonnegative numbers (-5sqrt6)(2sqrt3)

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Question 350866: Multiply and simplify. Assume that all variables represent nonnegative numbers
(-5sqrt6)(2sqrt3)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28-5sqrt%286%29%29%282sqrt%283%29%29
Since this expression is all multiplication and since multiplication is commutative and associative, we change change the grouping and/or order in any way we choose. So I am going to rearrage the factors so that the coefficients are together and grouped and the square roots are together and grouped:
%28%28-5%29%282%29%29%28sqrt%286%29%2Asqrt%283%29%29
The first part is easy to multiply. To multiply the square roots we need to know a basic property of radicals: root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29. We can use this to multiply square roots. Now we have:
%28-10%29%28sqrt%286%2A3%29%29
which simplifies to
-10sqrt%2818%29
We are almost done. Just like you should reduce/simplify answers that are fractions, you also should simplify square roots. To simplify a square root you look for perfect square factors in the radicand (the expression inside the square root). Since 18 has a perfect square factor, 18 = 9*2, we can simplify, using the property we used eariler:
-10sqrt%289%2A2%29
-10sqrt%289%29%2Asqrt%282%29
Since sqrt%289%29+=+3:
-10%2A3%2Asqrt%282%29
which simplifies to:
-30sqrt%282%29