Simplify Square Root of 86250

Here we will show you two methods that you can use to simplify the square root of 86250. In other words, we will show you how to find the square root of 86250 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.

√86250 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86250 to simplify the square root of 86250. 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 86250. The factors of 86250 are 1, 2, 3, 5, 6, 10, 15, 23, 25, 30, 46, 50, 69, 75, 115, 125, 138, 150, 230, 250, 345, 375, 575, 625, 690, 750, 1150, 1250, 1725, 1875, 2875, 3450, 3750, 5750, 8625, 14375, 17250, 28750, 43125, and 86250. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 86250 divided by the greatest perfect square from the list of all factors of 86250. We determined above that the greatest perfect square from the list of all factors of 86250 is 625. Furthermore, 86250 divided by 625 is 138, therefore B equals 138.

Now we have A and B and can get our answer to 86250 in its simplest radical form as follows:

√86250 = A√B

√86250 = 25√138

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86250 to simplify the square root of 86250 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 86250 and then take the square root of that product. The prime factors that multiply together to make 86250 are 2 x 3 x 5 x 5 x 5 x 5 x 23. 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 86250 by the number (A) squared. 25 squared is 625 and 86250 divided by 625 is 138. Therefore, B equals 138.

Once again we have A and B and can get our answer to 86250 in its simplest radical form as follows:

√86250 = A√B

√86250 = 25√138

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Simplify Square Root of 86251
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