Simplify Square Root of 86840

Here we will show you two methods that you can use to simplify the square root of 86840. In other words, we will show you how to find the square root of 86840 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.

√86840 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86840 to simplify the square root of 86840. 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 86840. The factors of 86840 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 167, 260, 334, 520, 668, 835, 1336, 1670, 2171, 3340, 4342, 6680, 8684, 10855, 17368, 21710, 43420, and 86840. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 86840 divided by the greatest perfect square from the list of all factors of 86840. We determined above that the greatest perfect square from the list of all factors of 86840 is 4. Furthermore, 86840 divided by 4 is 21710, therefore B equals 21710.

Now we have A and B and can get our answer to 86840 in its simplest radical form as follows:

√86840 = A√B

√86840 = 2√21710

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86840 to simplify the square root of 86840 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 86840 and then take the square root of that product. The prime factors that multiply together to make 86840 are 2 x 2 x 2 x 5 x 13 x 167. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 86840 by the number (A) squared. 2 squared is 4 and 86840 divided by 4 is 21710. Therefore, B equals 21710.

Once again we have A and B and can get our answer to 86840 in its simplest radical form as follows:

√86840 = A√B

√86840 = 2√21710

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Simplify Square Root of 86841
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