Simplify Square Root of 80352

Here we will show you two methods that you can use to simplify the square root of 80352. In other words, we will show you how to find the square root of 80352 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.

√80352 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80352 to simplify the square root of 80352. 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 80352. The factors of 80352 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 31, 32, 36, 48, 54, 62, 72, 81, 93, 96, 108, 124, 144, 162, 186, 216, 248, 279, 288, 324, 372, 432, 496, 558, 648, 744, 837, 864, 992, 1116, 1296, 1488, 1674, 2232, 2511, 2592, 2976, 3348, 4464, 5022, 6696, 8928, 10044, 13392, 20088, 26784, 40176, and 80352. Furthermore, the greatest perfect square on this list is 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Calculate 80352 divided by the greatest perfect square from the list of all factors of 80352. We determined above that the greatest perfect square from the list of all factors of 80352 is 1296. Furthermore, 80352 divided by 1296 is 62, therefore B equals 62.

Now we have A and B and can get our answer to 80352 in its simplest radical form as follows:

√80352 = A√B

√80352 = 36√62

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80352 to simplify the square root of 80352 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 80352 and then take the square root of that product. The prime factors that multiply together to make 80352 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 = 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Divide 80352 by the number (A) squared. 36 squared is 1296 and 80352 divided by 1296 is 62. Therefore, B equals 62.

Once again we have A and B and can get our answer to 80352 in its simplest radical form as follows:

√80352 = A√B

√80352 = 36√62

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