anonymous
  • anonymous
how do you simplify squaring square roots?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
it depends
TuringTest
  • TuringTest
um... like\[(\sqrt{x})^2\]?? Example please
anonymous
  • anonymous
well the first number is \[\sqrt{?}\]14

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anonymous
  • anonymous
replace the ? with 14
anonymous
  • anonymous
the square root of 14 is 3.7. so no you cannot because it is a decimal
anonymous
  • anonymous
so what would you put down as your answer
anonymous
  • anonymous
for that specific question i would put no. but it would work for instance, the squareroot of 16, which is 4, and the squareroot of 4 is 2. it varies from which number you are finding the square root for
TuringTest
  • TuringTest
In general you should try to factor the number under the root sign. \[\sqrt{14}=\sqrt{7\times 2}\]so this cannot be simplified. If however you had\[\sqrt{16}=\sqrt{2\times2\times2\times2}\]you can 'pull out' one copy of any number you have two copies of. In this case we have four 2's, so we can pull two 2's out of the sign and multiply them together:\[\sqrt{16}=\sqrt{2\times2\times2\times2}=2\times2=4\]A couple more examples for the sake of clarity:\[\sqrt{8}=\sqrt{2\times2\times2}=2\sqrt2\]\[\sqrt{108}=\sqrt{2\times2\times3\times3\times3}=(2\times3)\sqrt3=6\sqrt3\]

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