Simplify Square Root of 88900

Here we will show you two methods that you can use to simplify the square root of 88900. In other words, we will show you how to find the square root of 88900 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.

√88900 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88900 to simplify the square root of 88900. 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 88900. The factors of 88900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 127, 140, 175, 254, 350, 508, 635, 700, 889, 1270, 1778, 2540, 3175, 3556, 4445, 6350, 8890, 12700, 17780, 22225, 44450, and 88900. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 88900 divided by the greatest perfect square from the list of all factors of 88900. We determined above that the greatest perfect square from the list of all factors of 88900 is 100. Furthermore, 88900 divided by 100 is 889, therefore B equals 889.

Now we have A and B and can get our answer to 88900 in its simplest radical form as follows:

√88900 = A√B

√88900 = 10√889

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88900 to simplify the square root of 88900 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 88900 and then take the square root of that product. The prime factors that multiply together to make 88900 are 2 x 2 x 5 x 5 x 7 x 127. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 88900 by the number (A) squared. 10 squared is 100 and 88900 divided by 100 is 889. Therefore, B equals 889.

Once again we have A and B and can get our answer to 88900 in its simplest radical form as follows:

√88900 = A√B

√88900 = 10√889

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