Simplify Square Root of 36992

Here we will show you two methods that you can use to simplify the square root of 36992. In other words, we will show you how to find the square root of 36992 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.

√36992 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 36992 to simplify the square root of 36992. 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 36992. The factors of 36992 are 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 272, 289, 544, 578, 1088, 1156, 2176, 2312, 4624, 9248, 18496, and 36992. Furthermore, the greatest perfect square on this list is 18496 and the square root of 18496 is 136. Therefore, A equals 136.

B = Calculate 36992 divided by the greatest perfect square from the list of all factors of 36992. We determined above that the greatest perfect square from the list of all factors of 36992 is 18496. Furthermore, 36992 divided by 18496 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 36992 in its simplest radical form as follows:

√36992 = A√B

√36992 = 136√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 36992 to simplify the square root of 36992 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 36992 and then take the square root of that product. The prime factors that multiply together to make 36992 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 17 x 17 = 18496 and the square root of 18496 is 136. Therefore, A equals 136.

B = Divide 36992 by the number (A) squared. 136 squared is 18496 and 36992 divided by 18496 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 36992 in its simplest radical form as follows:

√36992 = A√B

√36992 = 136√2

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Simplify Square Root of 36993
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