Simplify Square Root of 24576

Here we will show you two methods that you can use to simplify the square root of 24576. In other words, we will show you how to find the square root of 24576 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.

√24576 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 24576 to simplify the square root of 24576. 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 24576. The factors of 24576 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, and 24576. Furthermore, the greatest perfect square on this list is 4096 and the square root of 4096 is 64. Therefore, A equals 64.

B = Calculate 24576 divided by the greatest perfect square from the list of all factors of 24576. We determined above that the greatest perfect square from the list of all factors of 24576 is 4096. Furthermore, 24576 divided by 4096 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 24576 in its simplest radical form as follows:

√24576 = A√B

√24576 = 64√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 24576 to simplify the square root of 24576 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 24576 and then take the square root of that product. The prime factors that multiply together to make 24576 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 4096 and the square root of 4096 is 64. Therefore, A equals 64.

B = Divide 24576 by the number (A) squared. 64 squared is 4096 and 24576 divided by 4096 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 24576 in its simplest radical form as follows:

√24576 = A√B

√24576 = 64√6

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Simplify Square Root of 24577
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