Simplify Square Root of 21456

Here we will show you two methods that you can use to simplify the square root of 21456. In other words, we will show you how to find the square root of 21456 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√21456 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 21456 to simplify the square root of 21456. 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 21456. The factors of 21456 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 149, 298, 447, 596, 894, 1192, 1341, 1788, 2384, 2682, 3576, 5364, 7152, 10728, and 21456. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 21456 divided by the greatest perfect square from the list of all factors of 21456. We determined above that the greatest perfect square from the list of all factors of 21456 is 144. Furthermore, 21456 divided by 144 is 149, therefore B equals 149.

Now we have A and B and can get our answer to 21456 in its simplest radical form as follows:

√21456 = A√B

√21456 = 12√149

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 21456 to simplify the square root of 21456 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 21456 and then take the square root of that product. The prime factors that multiply together to make 21456 are 2 x 2 x 2 x 2 x 3 x 3 x 149. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 21456 by the number (A) squared. 12 squared is 144 and 21456 divided by 144 is 149. Therefore, B equals 149.

Once again we have A and B and can get our answer to 21456 in its simplest radical form as follows:

√21456 = A√B

√21456 = 12√149

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Simplify Square Root of 21457
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