Simplify Square Root of 25012

Here we will show you two methods that you can use to simplify the square root of 25012. In other words, we will show you how to find the square root of 25012 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.

√25012 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 25012 to simplify the square root of 25012. 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 25012. The factors of 25012 are 1, 2, 4, 13, 26, 37, 52, 74, 148, 169, 338, 481, 676, 962, 1924, 6253, 12506, and 25012. Furthermore, the greatest perfect square on this list is 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Calculate 25012 divided by the greatest perfect square from the list of all factors of 25012. We determined above that the greatest perfect square from the list of all factors of 25012 is 676. Furthermore, 25012 divided by 676 is 37, therefore B equals 37.

Now we have A and B and can get our answer to 25012 in its simplest radical form as follows:

√25012 = A√B

√25012 = 26√37

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 25012 to simplify the square root of 25012 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 25012 and then take the square root of that product. The prime factors that multiply together to make 25012 are 2 x 2 x 13 x 13 x 37. When we strip out the pairs only, we get 2 x 2 x 13 x 13 = 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Divide 25012 by the number (A) squared. 26 squared is 676 and 25012 divided by 676 is 37. Therefore, B equals 37.

Once again we have A and B and can get our answer to 25012 in its simplest radical form as follows:

√25012 = A√B

√25012 = 26√37

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Simplify Square Root of 25013
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