Simplify Square Root of 63875

Here we will show you two methods that you can use to simplify the square root of 63875. In other words, we will show you how to find the square root of 63875 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.

√63875 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63875 to simplify the square root of 63875. 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 63875. The factors of 63875 are 1, 5, 7, 25, 35, 73, 125, 175, 365, 511, 875, 1825, 2555, 9125, 12775, and 63875. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 63875 divided by the greatest perfect square from the list of all factors of 63875. We determined above that the greatest perfect square from the list of all factors of 63875 is 25. Furthermore, 63875 divided by 25 is 2555, therefore B equals 2555.

Now we have A and B and can get our answer to 63875 in its simplest radical form as follows:

√63875 = A√B

√63875 = 5√2555

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63875 to simplify the square root of 63875 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 63875 and then take the square root of that product. The prime factors that multiply together to make 63875 are 5 x 5 x 5 x 7 x 73. 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 63875 by the number (A) squared. 5 squared is 25 and 63875 divided by 25 is 2555. Therefore, B equals 2555.

Once again we have A and B and can get our answer to 63875 in its simplest radical form as follows:

√63875 = A√B

√63875 = 5√2555

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Simplify Square Root of 63876
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