Simplify Square Root of 88750

Here we will show you two methods that you can use to simplify the square root of 88750. In other words, we will show you how to find the square root of 88750 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.

√88750 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88750 to simplify the square root of 88750. 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 88750. The factors of 88750 are 1, 2, 5, 10, 25, 50, 71, 125, 142, 250, 355, 625, 710, 1250, 1775, 3550, 8875, 17750, 44375, and 88750. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 88750 divided by the greatest perfect square from the list of all factors of 88750. We determined above that the greatest perfect square from the list of all factors of 88750 is 625. Furthermore, 88750 divided by 625 is 142, therefore B equals 142.

Now we have A and B and can get our answer to 88750 in its simplest radical form as follows:

√88750 = A√B

√88750 = 25√142

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88750 to simplify the square root of 88750 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 88750 and then take the square root of that product. The prime factors that multiply together to make 88750 are 2 x 5 x 5 x 5 x 5 x 71. 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 88750 by the number (A) squared. 25 squared is 625 and 88750 divided by 625 is 142. Therefore, B equals 142.

Once again we have A and B and can get our answer to 88750 in its simplest radical form as follows:

√88750 = A√B

√88750 = 25√142

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Simplify Square Root of 88751
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