Simplify Square Root of 84568

Here we will show you two methods that you can use to simplify the square root of 84568. In other words, we will show you how to find the square root of 84568 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.

√84568 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84568 to simplify the square root of 84568. 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 84568. The factors of 84568 are 1, 2, 4, 8, 11, 22, 31, 44, 62, 88, 124, 248, 341, 682, 961, 1364, 1922, 2728, 3844, 7688, 10571, 21142, 42284, and 84568. Furthermore, the greatest perfect square on this list is 3844 and the square root of 3844 is 62. Therefore, A equals 62.

B = Calculate 84568 divided by the greatest perfect square from the list of all factors of 84568. We determined above that the greatest perfect square from the list of all factors of 84568 is 3844. Furthermore, 84568 divided by 3844 is 22, therefore B equals 22.

Now we have A and B and can get our answer to 84568 in its simplest radical form as follows:

√84568 = A√B

√84568 = 62√22

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84568 to simplify the square root of 84568 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 84568 and then take the square root of that product. The prime factors that multiply together to make 84568 are 2 x 2 x 2 x 11 x 31 x 31. When we strip out the pairs only, we get 2 x 2 x 31 x 31 = 3844 and the square root of 3844 is 62. Therefore, A equals 62.

B = Divide 84568 by the number (A) squared. 62 squared is 3844 and 84568 divided by 3844 is 22. Therefore, B equals 22.

Once again we have A and B and can get our answer to 84568 in its simplest radical form as follows:

√84568 = A√B

√84568 = 62√22

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