Simplify Square Root of 76472

Here we will show you two methods that you can use to simplify the square root of 76472. In other words, we will show you how to find the square root of 76472 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.

√76472 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 76472 to simplify the square root of 76472. 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 76472. The factors of 76472 are 1, 2, 4, 8, 11, 22, 44, 79, 88, 121, 158, 242, 316, 484, 632, 869, 968, 1738, 3476, 6952, 9559, 19118, 38236, and 76472. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 76472 divided by the greatest perfect square from the list of all factors of 76472. We determined above that the greatest perfect square from the list of all factors of 76472 is 484. Furthermore, 76472 divided by 484 is 158, therefore B equals 158.

Now we have A and B and can get our answer to 76472 in its simplest radical form as follows:

√76472 = A√B

√76472 = 22√158

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 76472 to simplify the square root of 76472 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 76472 and then take the square root of that product. The prime factors that multiply together to make 76472 are 2 x 2 x 2 x 11 x 11 x 79. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 76472 by the number (A) squared. 22 squared is 484 and 76472 divided by 484 is 158. Therefore, B equals 158.

Once again we have A and B and can get our answer to 76472 in its simplest radical form as follows:

√76472 = A√B

√76472 = 22√158

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