Simplify Square Root of 86490

Here we will show you two methods that you can use to simplify the square root of 86490. In other words, we will show you how to find the square root of 86490 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.

√86490 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86490 to simplify the square root of 86490. 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 86490. The factors of 86490 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 31, 45, 62, 90, 93, 155, 186, 279, 310, 465, 558, 930, 961, 1395, 1922, 2790, 2883, 4805, 5766, 8649, 9610, 14415, 17298, 28830, 43245, and 86490. Furthermore, the greatest perfect square on this list is 8649 and the square root of 8649 is 93. Therefore, A equals 93.

B = Calculate 86490 divided by the greatest perfect square from the list of all factors of 86490. We determined above that the greatest perfect square from the list of all factors of 86490 is 8649. Furthermore, 86490 divided by 8649 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 86490 in its simplest radical form as follows:

√86490 = A√B

√86490 = 93√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86490 to simplify the square root of 86490 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 86490 and then take the square root of that product. The prime factors that multiply together to make 86490 are 2 x 3 x 3 x 5 x 31 x 31. When we strip out the pairs only, we get 3 x 3 x 31 x 31 = 8649 and the square root of 8649 is 93. Therefore, A equals 93.

B = Divide 86490 by the number (A) squared. 93 squared is 8649 and 86490 divided by 8649 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 86490 in its simplest radical form as follows:

√86490 = A√B

√86490 = 93√10

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Simplify Square Root of 86491
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