Simplify Square Root of 3712

Here we will show you two methods that you can use to simplify the square root of 3712. In other words, we will show you how to find the square root of 3712 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.

√3712 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 3712 to simplify the square root of 3712. 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 3712. The factors of 3712 are 1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 464, 928, 1856, and 3712. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 3712 divided by the greatest perfect square from the list of all factors of 3712. We determined above that the greatest perfect square from the list of all factors of 3712 is 64. Furthermore, 3712 divided by 64 is 58, therefore B equals 58.

Now we have A and B and can get our answer to 3712 in its simplest radical form as follows:

√3712 = A√B

√3712 = 8√58

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 3712 to simplify the square root of 3712 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 3712 and then take the square root of that product. The prime factors that multiply together to make 3712 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 29. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 3712 by the number (A) squared. 8 squared is 64 and 3712 divided by 64 is 58. Therefore, B equals 58.

Once again we have A and B and can get our answer to 3712 in its simplest radical form as follows:

√3712 = A√B

√3712 = 8√58

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Simplify Square Root of 3713
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