Simplify Square Root of 86700

Here we will show you two methods that you can use to simplify the square root of 86700. In other words, we will show you how to find the square root of 86700 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.

√86700 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86700 to simplify the square root of 86700. 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 86700. The factors of 86700 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 50, 51, 60, 68, 75, 85, 100, 102, 150, 170, 204, 255, 289, 300, 340, 425, 510, 578, 850, 867, 1020, 1156, 1275, 1445, 1700, 1734, 2550, 2890, 3468, 4335, 5100, 5780, 7225, 8670, 14450, 17340, 21675, 28900, 43350, and 86700. Furthermore, the greatest perfect square on this list is 28900 and the square root of 28900 is 170. Therefore, A equals 170.

B = Calculate 86700 divided by the greatest perfect square from the list of all factors of 86700. We determined above that the greatest perfect square from the list of all factors of 86700 is 28900. Furthermore, 86700 divided by 28900 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 86700 in its simplest radical form as follows:

√86700 = A√B

√86700 = 170√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86700 to simplify the square root of 86700 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 86700 and then take the square root of that product. The prime factors that multiply together to make 86700 are 2 x 2 x 3 x 5 x 5 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 5 x 5 x 17 x 17 = 28900 and the square root of 28900 is 170. Therefore, A equals 170.

B = Divide 86700 by the number (A) squared. 170 squared is 28900 and 86700 divided by 28900 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 86700 in its simplest radical form as follows:

√86700 = A√B

√86700 = 170√3

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