Simplify Square Root of 65625

Here we will show you two methods that you can use to simplify the square root of 65625. In other words, we will show you how to find the square root of 65625 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.

√65625 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65625 to simplify the square root of 65625. 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 65625. The factors of 65625 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 625, 875, 1875, 2625, 3125, 4375, 9375, 13125, 21875, and 65625. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 65625 divided by the greatest perfect square from the list of all factors of 65625. We determined above that the greatest perfect square from the list of all factors of 65625 is 625. Furthermore, 65625 divided by 625 is 105, therefore B equals 105.

Now we have A and B and can get our answer to 65625 in its simplest radical form as follows:

√65625 = A√B

√65625 = 25√105

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65625 to simplify the square root of 65625 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 65625 and then take the square root of that product. The prime factors that multiply together to make 65625 are 3 x 5 x 5 x 5 x 5 x 5 x 7. When we strip out the pairs only, we get 5 x 5 x 5 x 5 = 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Divide 65625 by the number (A) squared. 25 squared is 625 and 65625 divided by 625 is 105. Therefore, B equals 105.

Once again we have A and B and can get our answer to 65625 in its simplest radical form as follows:

√65625 = A√B

√65625 = 25√105

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Simplify Square Root of 65626
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