Simplify Square Root of 85456

Here we will show you two methods that you can use to simplify the square root of 85456. In other words, we will show you how to find the square root of 85456 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.

√85456 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85456 to simplify the square root of 85456. 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 85456. The factors of 85456 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 109, 112, 196, 218, 392, 436, 763, 784, 872, 1526, 1744, 3052, 5341, 6104, 10682, 12208, 21364, 42728, and 85456. Furthermore, the greatest perfect square on this list is 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Calculate 85456 divided by the greatest perfect square from the list of all factors of 85456. We determined above that the greatest perfect square from the list of all factors of 85456 is 784. Furthermore, 85456 divided by 784 is 109, therefore B equals 109.

Now we have A and B and can get our answer to 85456 in its simplest radical form as follows:

√85456 = A√B

√85456 = 28√109

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85456 to simplify the square root of 85456 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 85456 and then take the square root of that product. The prime factors that multiply together to make 85456 are 2 x 2 x 2 x 2 x 7 x 7 x 109. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 7 x 7 = 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Divide 85456 by the number (A) squared. 28 squared is 784 and 85456 divided by 784 is 109. Therefore, B equals 109.

Once again we have A and B and can get our answer to 85456 in its simplest radical form as follows:

√85456 = A√B

√85456 = 28√109

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