Simplify Square Root of 32448

Here we will show you two methods that you can use to simplify the square root of 32448. In other words, we will show you how to find the square root of 32448 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.

√32448 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32448 to simplify the square root of 32448. 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 32448. The factors of 32448 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 156, 169, 192, 208, 312, 338, 416, 507, 624, 676, 832, 1014, 1248, 1352, 2028, 2496, 2704, 4056, 5408, 8112, 10816, 16224, and 32448. Furthermore, the greatest perfect square on this list is 10816 and the square root of 10816 is 104. Therefore, A equals 104.

B = Calculate 32448 divided by the greatest perfect square from the list of all factors of 32448. We determined above that the greatest perfect square from the list of all factors of 32448 is 10816. Furthermore, 32448 divided by 10816 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 32448 in its simplest radical form as follows:

√32448 = A√B

√32448 = 104√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 32448 to simplify the square root of 32448 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 32448 and then take the square root of that product. The prime factors that multiply together to make 32448 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 13 x 13 = 10816 and the square root of 10816 is 104. Therefore, A equals 104.

B = Divide 32448 by the number (A) squared. 104 squared is 10816 and 32448 divided by 10816 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 32448 in its simplest radical form as follows:

√32448 = A√B

√32448 = 104√3

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