## anonymous 5 years ago how do you simplify squaring square roots?

1. anonymous

it depends

2. TuringTest

um... like$(\sqrt{x})^2$?? Example please

3. anonymous

well the first number is $\sqrt{?}$14

4. anonymous

replace the ? with 14

5. anonymous

the square root of 14 is 3.7. so no you cannot because it is a decimal

6. anonymous

7. 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

8. 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$