Simplify Square Root of 5312

Here we will show you two methods that you can use to simplify the square root of 5312. In other words, we will show you how to find the square root of 5312 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.

√5312 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 5312 to simplify the square root of 5312. 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 5312. The factors of 5312 are 1, 2, 4, 8, 16, 32, 64, 83, 166, 332, 664, 1328, 2656, and 5312. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 5312 divided by the greatest perfect square from the list of all factors of 5312. We determined above that the greatest perfect square from the list of all factors of 5312 is 64. Furthermore, 5312 divided by 64 is 83, therefore B equals 83.

Now we have A and B and can get our answer to 5312 in its simplest radical form as follows:

√5312 = A√B

√5312 = 8√83

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 5312 to simplify the square root of 5312 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 5312 and then take the square root of that product. The prime factors that multiply together to make 5312 are 2 x 2 x 2 x 2 x 2 x 2 x 83. 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 5312 by the number (A) squared. 8 squared is 64 and 5312 divided by 64 is 83. Therefore, B equals 83.

Once again we have A and B and can get our answer to 5312 in its simplest radical form as follows:

√5312 = A√B

√5312 = 8√83

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Simplify Square Root of 5313
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