Simplify Square Root of 12475

Here we will show you two methods that you can use to simplify the square root of 12475. In other words, we will show you how to find the square root of 12475 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.

√12475 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12475 to simplify the square root of 12475. 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 12475. The factors of 12475 are 1, 5, 25, 499, 2495, and 12475. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 12475 divided by the greatest perfect square from the list of all factors of 12475. We determined above that the greatest perfect square from the list of all factors of 12475 is 25. Furthermore, 12475 divided by 25 is 499, therefore B equals 499.

Now we have A and B and can get our answer to 12475 in its simplest radical form as follows:

√12475 = A√B

√12475 = 5√499

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12475 to simplify the square root of 12475 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 12475 and then take the square root of that product. The prime factors that multiply together to make 12475 are 5 x 5 x 499. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 12475 by the number (A) squared. 5 squared is 25 and 12475 divided by 25 is 499. Therefore, B equals 499.

Once again we have A and B and can get our answer to 12475 in its simplest radical form as follows:

√12475 = A√B

√12475 = 5√499

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