Simplify Square Root of 87846

Here we will show you two methods that you can use to simplify the square root of 87846. In other words, we will show you how to find the square root of 87846 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.

√87846 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 87846 to simplify the square root of 87846. 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 87846. The factors of 87846 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726, 1331, 2662, 3993, 7986, 14641, 29282, 43923, and 87846. Furthermore, the greatest perfect square on this list is 14641 and the square root of 14641 is 121. Therefore, A equals 121.

B = Calculate 87846 divided by the greatest perfect square from the list of all factors of 87846. We determined above that the greatest perfect square from the list of all factors of 87846 is 14641. Furthermore, 87846 divided by 14641 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 87846 in its simplest radical form as follows:

√87846 = A√B

√87846 = 121√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 87846 to simplify the square root of 87846 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 87846 and then take the square root of that product. The prime factors that multiply together to make 87846 are 2 x 3 x 11 x 11 x 11 x 11. When we strip out the pairs only, we get 11 x 11 x 11 x 11 = 14641 and the square root of 14641 is 121. Therefore, A equals 121.

B = Divide 87846 by the number (A) squared. 121 squared is 14641 and 87846 divided by 14641 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 87846 in its simplest radical form as follows:

√87846 = A√B

√87846 = 121√6

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