Simplify Square Root of 3456

Here we will show you two methods that you can use to simplify the square root of 3456. In other words, we will show you how to find the square root of 3456 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.

√3456 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 3456 to simplify the square root of 3456. 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 3456. The factors of 3456 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 288, 384, 432, 576, 864, 1152, 1728, and 3456. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 3456 divided by the greatest perfect square from the list of all factors of 3456. We determined above that the greatest perfect square from the list of all factors of 3456 is 576. Furthermore, 3456 divided by 576 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 3456 in its simplest radical form as follows:

√3456 = A√B

√3456 = 24√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 3456 to simplify the square root of 3456 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 3456 and then take the square root of that product. The prime factors that multiply together to make 3456 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 3456 by the number (A) squared. 24 squared is 576 and 3456 divided by 576 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 3456 in its simplest radical form as follows:

√3456 = A√B

√3456 = 24√6

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