# What is the square root of 216?

What is the square root of 216?
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jean2098
Explanation:
Start by factoring 216 completely. Just simplify it afterwards.
$\sqrt{216}$
$=\sqrt{2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 3}$
$=\sqrt{{2}^{2}\cdot 2\cdot {3}^{2}\cdot 3}$
$=\left(2\cdot 3\right)\sqrt{2\cdot 3}$
$=6\sqrt{6}$

stomachdm
Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 216 to simplify the square root of 216. This is how to calculate A and B using this method:
A = Calculate the square root of the greatest perfect square from the list of all factors of 216. The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.
B = Calculate 216 divided by the greatest perfect square from the list of all factors of 216. We determined above that the greatest perfect square from the list of all factors of 216 is 36. Furthermore, 216 divided by 36 is 6, therefore B equals 6.
Now we have A and B and can get our answer to 216 in its simplest radical form as follows:
$\sqrt{216}=A\sqrt{B}$
$\sqrt{216}=6\sqrt{6}$