Simplify Square Root of 78732

Here we will show you two methods that you can use to simplify the square root of 78732. In other words, we will show you how to find the square root of 78732 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.

√78732 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78732 to simplify the square root of 78732. 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 78732. The factors of 78732 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 729, 972, 1458, 2187, 2916, 4374, 6561, 8748, 13122, 19683, 26244, 39366, and 78732. Furthermore, the greatest perfect square on this list is 26244 and the square root of 26244 is 162. Therefore, A equals 162.

B = Calculate 78732 divided by the greatest perfect square from the list of all factors of 78732. We determined above that the greatest perfect square from the list of all factors of 78732 is 26244. Furthermore, 78732 divided by 26244 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 78732 in its simplest radical form as follows:

√78732 = A√B

√78732 = 162√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78732 to simplify the square root of 78732 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 78732 and then take the square root of that product. The prime factors that multiply together to make 78732 are 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 26244 and the square root of 26244 is 162. Therefore, A equals 162.

B = Divide 78732 by the number (A) squared. 162 squared is 26244 and 78732 divided by 26244 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 78732 in its simplest radical form as follows:

√78732 = A√B

√78732 = 162√3

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