Simplify Square Root of 12675

Here we will show you two methods that you can use to simplify the square root of 12675. In other words, we will show you how to find the square root of 12675 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.

√12675 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12675 to simplify the square root of 12675. 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 12675. The factors of 12675 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 169, 195, 325, 507, 845, 975, 2535, 4225, and 12675. Furthermore, the greatest perfect square on this list is 4225 and the square root of 4225 is 65. Therefore, A equals 65.

B = Calculate 12675 divided by the greatest perfect square from the list of all factors of 12675. We determined above that the greatest perfect square from the list of all factors of 12675 is 4225. Furthermore, 12675 divided by 4225 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 12675 in its simplest radical form as follows:

√12675 = A√B

√12675 = 65√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12675 to simplify the square root of 12675 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 12675 and then take the square root of that product. The prime factors that multiply together to make 12675 are 3 x 5 x 5 x 13 x 13. When we strip out the pairs only, we get 5 x 5 x 13 x 13 = 4225 and the square root of 4225 is 65. Therefore, A equals 65.

B = Divide 12675 by the number (A) squared. 65 squared is 4225 and 12675 divided by 4225 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 12675 in its simplest radical form as follows:

√12675 = A√B

√12675 = 65√3

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Simplify Square Root of 12676
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