Simplify Square Root of 80724

Here we will show you two methods that you can use to simplify the square root of 80724. In other words, we will show you how to find the square root of 80724 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.

√80724 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80724 to simplify the square root of 80724. 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 80724. The factors of 80724 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 31, 42, 62, 84, 93, 124, 186, 217, 372, 434, 651, 868, 961, 1302, 1922, 2604, 2883, 3844, 5766, 6727, 11532, 13454, 20181, 26908, 40362, and 80724. Furthermore, the greatest perfect square on this list is 3844 and the square root of 3844 is 62. Therefore, A equals 62.

B = Calculate 80724 divided by the greatest perfect square from the list of all factors of 80724. We determined above that the greatest perfect square from the list of all factors of 80724 is 3844. Furthermore, 80724 divided by 3844 is 21, therefore B equals 21.

Now we have A and B and can get our answer to 80724 in its simplest radical form as follows:

√80724 = A√B

√80724 = 62√21

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80724 to simplify the square root of 80724 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 80724 and then take the square root of that product. The prime factors that multiply together to make 80724 are 2 x 2 x 3 x 7 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 80724 by the number (A) squared. 62 squared is 3844 and 80724 divided by 3844 is 21. Therefore, B equals 21.

Once again we have A and B and can get our answer to 80724 in its simplest radical form as follows:

√80724 = A√B

√80724 = 62√21

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