Simplify Square Root of 76664

Here we will show you two methods that you can use to simplify the square root of 76664. In other words, we will show you how to find the square root of 76664 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.

√76664 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 76664 to simplify the square root of 76664. 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 76664. The factors of 76664 are 1, 2, 4, 7, 8, 14, 28, 37, 56, 74, 148, 259, 296, 518, 1036, 1369, 2072, 2738, 5476, 9583, 10952, 19166, 38332, and 76664. Furthermore, the greatest perfect square on this list is 5476 and the square root of 5476 is 74. Therefore, A equals 74.

B = Calculate 76664 divided by the greatest perfect square from the list of all factors of 76664. We determined above that the greatest perfect square from the list of all factors of 76664 is 5476. Furthermore, 76664 divided by 5476 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 76664 in its simplest radical form as follows:

√76664 = A√B

√76664 = 74√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 76664 to simplify the square root of 76664 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 76664 and then take the square root of that product. The prime factors that multiply together to make 76664 are 2 x 2 x 2 x 7 x 37 x 37. When we strip out the pairs only, we get 2 x 2 x 37 x 37 = 5476 and the square root of 5476 is 74. Therefore, A equals 74.

B = Divide 76664 by the number (A) squared. 74 squared is 5476 and 76664 divided by 5476 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 76664 in its simplest radical form as follows:

√76664 = A√B

√76664 = 74√14

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