Simplify Square Root of 12992

Here we will show you two methods that you can use to simplify the square root of 12992. In other words, we will show you how to find the square root of 12992 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.

√12992 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12992 to simplify the square root of 12992. 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 12992. The factors of 12992 are 1, 2, 4, 7, 8, 14, 16, 28, 29, 32, 56, 58, 64, 112, 116, 203, 224, 232, 406, 448, 464, 812, 928, 1624, 1856, 3248, 6496, and 12992. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 12992 divided by the greatest perfect square from the list of all factors of 12992. We determined above that the greatest perfect square from the list of all factors of 12992 is 64. Furthermore, 12992 divided by 64 is 203, therefore B equals 203.

Now we have A and B and can get our answer to 12992 in its simplest radical form as follows:

√12992 = A√B

√12992 = 8√203

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12992 to simplify the square root of 12992 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 12992 and then take the square root of that product. The prime factors that multiply together to make 12992 are 2 x 2 x 2 x 2 x 2 x 2 x 7 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 12992 by the number (A) squared. 8 squared is 64 and 12992 divided by 64 is 203. Therefore, B equals 203.

Once again we have A and B and can get our answer to 12992 in its simplest radical form as follows:

√12992 = A√B

√12992 = 8√203

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Simplify Square Root of 12993
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