SOLUTION: please simplify this expression: 5 square root 15 times (-2 square root 3)

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Question 389875: please simplify this expression:
5 square root 15 times (-2 square root 3)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
5sqrt%2815%29%2A%28-2sqrt%283%29%29
This expression is all multiplication. So we can use the Commutative and Associative properties to rearrange the order and grouping to:
%285%2A%28-2%29%29%28sqrt%2815%29%2Asqrt%283%29%29
Multiplying the first part is simple. We use the property of radicals, root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29, to multiply the square roots:
-10sqrt%2845%29
Last of all we simplify. We can simplify sqrt%2845%29 because it has a perfect square factor, 9:
-10sqrt%289%2A5%29
Now we can use the property of radicals (from right to left) to separate the factors into their won square roots:
-10sqrt%289%29%2Asqrt%285%29
Since sqrt%289%29+=+3 this becomes:
-10%2A3%2Asqrt%285%29
which simplifies to:
-30sqrt%285%29