Simplify Square Root of 48672

Here we will show you two methods that you can use to simplify the square root of 48672. In other words, we will show you how to find the square root of 48672 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.

√48672 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48672 to simplify the square root of 48672. 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 48672. The factors of 48672 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 72, 78, 96, 104, 117, 144, 156, 169, 208, 234, 288, 312, 338, 416, 468, 507, 624, 676, 936, 1014, 1248, 1352, 1521, 1872, 2028, 2704, 3042, 3744, 4056, 5408, 6084, 8112, 12168, 16224, 24336, and 48672. Furthermore, the greatest perfect square on this list is 24336 and the square root of 24336 is 156. Therefore, A equals 156.

B = Calculate 48672 divided by the greatest perfect square from the list of all factors of 48672. We determined above that the greatest perfect square from the list of all factors of 48672 is 24336. Furthermore, 48672 divided by 24336 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 48672 in its simplest radical form as follows:

√48672 = A√B

√48672 = 156√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48672 to simplify the square root of 48672 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 48672 and then take the square root of that product. The prime factors that multiply together to make 48672 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 13 x 13 = 24336 and the square root of 24336 is 156. Therefore, A equals 156.

B = Divide 48672 by the number (A) squared. 156 squared is 24336 and 48672 divided by 24336 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 48672 in its simplest radical form as follows:

√48672 = A√B

√48672 = 156√2

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