Simplify Square Root of 12798

Here we will show you two methods that you can use to simplify the square root of 12798. In other words, we will show you how to find the square root of 12798 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.

√12798 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12798 to simplify the square root of 12798. 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 12798. The factors of 12798 are 1, 2, 3, 6, 9, 18, 27, 54, 79, 81, 158, 162, 237, 474, 711, 1422, 2133, 4266, 6399, and 12798. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 12798 divided by the greatest perfect square from the list of all factors of 12798. We determined above that the greatest perfect square from the list of all factors of 12798 is 81. Furthermore, 12798 divided by 81 is 158, therefore B equals 158.

Now we have A and B and can get our answer to 12798 in its simplest radical form as follows:

√12798 = A√B

√12798 = 9√158

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12798 to simplify the square root of 12798 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 12798 and then take the square root of that product. The prime factors that multiply together to make 12798 are 2 x 3 x 3 x 3 x 3 x 79. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 12798 by the number (A) squared. 9 squared is 81 and 12798 divided by 81 is 158. Therefore, B equals 158.

Once again we have A and B and can get our answer to 12798 in its simplest radical form as follows:

√12798 = A√B

√12798 = 9√158

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Simplify Square Root of 12799
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