tripiverded9

Answered question

2021-12-16

What is the square root of 216?

Answer & Explanation

jean2098

Beginner2021-12-17Added 38 answers

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

Beginner2021-12-18Added 33 answers

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:
$\sqrt{216}=A\sqrt{B}$
$\sqrt{216}=6\sqrt{6}$

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?