Simplify Square Root of 76788

Here we will show you two methods that you can use to simplify the square root of 76788. In other words, we will show you how to find the square root of 76788 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.

√76788 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 76788 to simplify the square root of 76788. 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 76788. The factors of 76788 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 79, 81, 108, 158, 162, 237, 243, 316, 324, 474, 486, 711, 948, 972, 1422, 2133, 2844, 4266, 6399, 8532, 12798, 19197, 25596, 38394, and 76788. Furthermore, the greatest perfect square on this list is 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Calculate 76788 divided by the greatest perfect square from the list of all factors of 76788. We determined above that the greatest perfect square from the list of all factors of 76788 is 324. Furthermore, 76788 divided by 324 is 237, therefore B equals 237.

Now we have A and B and can get our answer to 76788 in its simplest radical form as follows:

√76788 = A√B

√76788 = 18√237

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 76788 to simplify the square root of 76788 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 76788 and then take the square root of that product. The prime factors that multiply together to make 76788 are 2 x 2 x 3 x 3 x 3 x 3 x 3 x 79. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 = 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Divide 76788 by the number (A) squared. 18 squared is 324 and 76788 divided by 324 is 237. Therefore, B equals 237.

Once again we have A and B and can get our answer to 76788 in its simplest radical form as follows:

√76788 = A√B

√76788 = 18√237

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