Simplify Square Root of 81925

Here we will show you two methods that you can use to simplify the square root of 81925. In other words, we will show you how to find the square root of 81925 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.

√81925 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81925 to simplify the square root of 81925. 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 81925. The factors of 81925 are 1, 5, 25, 29, 113, 145, 565, 725, 2825, 3277, 16385, and 81925. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 81925 divided by the greatest perfect square from the list of all factors of 81925. We determined above that the greatest perfect square from the list of all factors of 81925 is 25. Furthermore, 81925 divided by 25 is 3277, therefore B equals 3277.

Now we have A and B and can get our answer to 81925 in its simplest radical form as follows:

√81925 = A√B

√81925 = 5√3277

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81925 to simplify the square root of 81925 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 81925 and then take the square root of that product. The prime factors that multiply together to make 81925 are 5 x 5 x 29 x 113. 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 81925 by the number (A) squared. 5 squared is 25 and 81925 divided by 25 is 3277. Therefore, B equals 3277.

Once again we have A and B and can get our answer to 81925 in its simplest radical form as follows:

√81925 = A√B

√81925 = 5√3277

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Simplify Square Root of 81926
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