Simplify Square Root of 58725

Here we will show you two methods that you can use to simplify the square root of 58725. In other words, we will show you how to find the square root of 58725 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.

√58725 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58725 to simplify the square root of 58725. 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 58725. The factors of 58725 are 1, 3, 5, 9, 15, 25, 27, 29, 45, 75, 81, 87, 135, 145, 225, 261, 405, 435, 675, 725, 783, 1305, 2025, 2175, 2349, 3915, 6525, 11745, 19575, and 58725. Furthermore, the greatest perfect square on this list is 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Calculate 58725 divided by the greatest perfect square from the list of all factors of 58725. We determined above that the greatest perfect square from the list of all factors of 58725 is 2025. Furthermore, 58725 divided by 2025 is 29, therefore B equals 29.

Now we have A and B and can get our answer to 58725 in its simplest radical form as follows:

√58725 = A√B

√58725 = 45√29

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58725 to simplify the square root of 58725 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 58725 and then take the square root of that product. The prime factors that multiply together to make 58725 are 3 x 3 x 3 x 3 x 5 x 5 x 29. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 5 x 5 = 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Divide 58725 by the number (A) squared. 45 squared is 2025 and 58725 divided by 2025 is 29. Therefore, B equals 29.

Once again we have A and B and can get our answer to 58725 in its simplest radical form as follows:

√58725 = A√B

√58725 = 45√29

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Simplify Square Root of 58726
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