SOLUTION: How do I simplify -4 times the square root of 24

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Question 368718: How do I simplify -4 times the square root of 24
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
-4sqrt%2824%29
Simplifying square roots is done by finding perfect square factors (other than 1) of the radicand (the expression inside a radical). If there are no perfect square factors of the radicand, the square root cannot be simplified. So we will be looking for perfect square factors of your radicand, 24. Among the factors of 24, only one is a perfect suqare: 4. So we rewrite the square root in a factored form, using the perfect square factor:
-4sqrt%284%2A6%29
Next we use a property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29 to separate the factors into their own square roots:
-4sqrt%284%29%2Asqrt%286%29
Now that the perfect square factor is in its own square root, we can replace it. Since sqrt%284%29+=+2 we will replace it with 2:
-4%2A2%2Asqrt%286%29
Last of all we multiply the -4 and the 2:
-8%2Asqrt%286%29