Question 496835: how do i get from:
√36 + 81
to:
3√13?
i don't understand how to simplify radicals or square roots or whatever they are called.
Found 2 solutions by josmiceli, lmeeks54:
Answer by josmiceli(19441)   (Show Source):
Answer by lmeeks54(111)  (Show Source):
You can put this solution on YOUR website! Simplifying radicals (roots) is done by factoring the number inside the radical. Whenever any of the factors is a perfect square (the square root is an integer), then that root can come out of the radical.
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I'll illustrate all this in a second, but first, there is a problem with your problem.
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36 + 81 = 117
sqrt(117) = 10.81665
3 x sqrt(13) = 10.81665
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117 = 9 x 13
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To work this by simplifying the radicals, we rewrite sqrt(117) = sqrt(9x13)
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Since 9 is a perfect square, it can be rewritten as 3 x 3, thus the sqrt(117) could be rewritten:
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sqrt(3 x 3 x 13)
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Following what I wrote earlier about a perfect square factor (in this case, 9) inside the radical can be be brought outside as its square root (in this case, 3), we get the 3 x sqrt(13) found in your problem.
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Now the problem with your problem (and it might be trying to get the symbols and equations written correctly in the input window) is that we need to the beginning of the problem to be asking you for the sqrt(117) to work the simplifying radicals steps to end up with 3 x sqrt(13).
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Does this make sense?
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Cheers,
Lee
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