Simplify Square Root of 85176

Here we will show you two methods that you can use to simplify the square root of 85176. In other words, we will show you how to find the square root of 85176 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.

√85176 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85176 to simplify the square root of 85176. 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 85176. The factors of 85176 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 18, 21, 24, 26, 28, 36, 39, 42, 52, 56, 63, 72, 78, 84, 91, 104, 117, 126, 156, 168, 169, 182, 234, 252, 273, 312, 338, 364, 468, 504, 507, 546, 676, 728, 819, 936, 1014, 1092, 1183, 1352, 1521, 1638, 2028, 2184, 2366, 3042, 3276, 3549, 4056, 4732, 6084, 6552, 7098, 9464, 10647, 12168, 14196, 21294, 28392, 42588, and 85176. Furthermore, the greatest perfect square on this list is 6084 and the square root of 6084 is 78. Therefore, A equals 78.

B = Calculate 85176 divided by the greatest perfect square from the list of all factors of 85176. We determined above that the greatest perfect square from the list of all factors of 85176 is 6084. Furthermore, 85176 divided by 6084 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 85176 in its simplest radical form as follows:

√85176 = A√B

√85176 = 78√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85176 to simplify the square root of 85176 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 85176 and then take the square root of that product. The prime factors that multiply together to make 85176 are 2 x 2 x 2 x 3 x 3 x 7 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 13 x 13 = 6084 and the square root of 6084 is 78. Therefore, A equals 78.

B = Divide 85176 by the number (A) squared. 78 squared is 6084 and 85176 divided by 6084 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 85176 in its simplest radical form as follows:

√85176 = A√B

√85176 = 78√14

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 85177
Here is the next square root on our list that we have simplifed for you.