SOLUTION: Simplify: square root of 500

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Question 86811: Simplify:
square root of 500
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
square root of 500
sqrt(500) = [sqrt100]
=10 sqrt(5)
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cheers,
Stan H.

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Since 500 is an even number you know that it is divisible by 2. Therefore, you can write
it as 500+=+250+%2A+2
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But 250 is also even and divisible by 2. So 250 can be replaced by 125 * 2. Therefore,
you can replace 500 by 125*2*2 which is equivalent to 500+=+125%2A2%5E2
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Then 125+=+5%2A5%2A5+=+5%2A5%5E2. So if you substitute 5%2A5%5E2 for 125 you get:
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500+=+5%2A5%5E2%2A2%5E2
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Taking the square root of all three terms in this multiplication string results in:
.

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So the simplified form of sqrt%28500%29 is 10%2Asqrt%285%29
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Had you recognized it earlier, you could have written:
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sqrt%28500%29+=+sqrt%28100%2A5%29+=+sqrt%28100%29%2Asqrt%285%29+=+10%2Asqrt%285%29
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much quicker, but not as much practice as the long way.
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Hope this helps you to see how square root problems such as this one can be simplified.
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