Simplify Square Root of 2312

Here we will show you two methods that you can use to simplify the square root of 2312. In other words, we will show you how to find the square root of 2312 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.

√2312 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2312 to simplify the square root of 2312. 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 2312. The factors of 2312 are 1, 2, 4, 8, 17, 34, 68, 136, 289, 578, 1156, and 2312. Furthermore, the greatest perfect square on this list is 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Calculate 2312 divided by the greatest perfect square from the list of all factors of 2312. We determined above that the greatest perfect square from the list of all factors of 2312 is 1156. Furthermore, 2312 divided by 1156 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 2312 in its simplest radical form as follows:

√2312 = A√B

√2312 = 34√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2312 to simplify the square root of 2312 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 2312 and then take the square root of that product. The prime factors that multiply together to make 2312 are 2 x 2 x 2 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 17 x 17 = 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Divide 2312 by the number (A) squared. 34 squared is 1156 and 2312 divided by 1156 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 2312 in its simplest radical form as follows:

√2312 = A√B

√2312 = 34√2

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Simplify Square Root of 2313
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