Simplify Square Root of 32076

Here we will show you two methods that you can use to simplify the square root of 32076. In other words, we will show you how to find the square root of 32076 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.

√32076 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32076 to simplify the square root of 32076. 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 32076. The factors of 32076 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 81, 99, 108, 132, 162, 198, 243, 297, 324, 396, 486, 594, 729, 891, 972, 1188, 1458, 1782, 2673, 2916, 3564, 5346, 8019, 10692, 16038, and 32076. Furthermore, the greatest perfect square on this list is 2916 and the square root of 2916 is 54. Therefore, A equals 54.

B = Calculate 32076 divided by the greatest perfect square from the list of all factors of 32076. We determined above that the greatest perfect square from the list of all factors of 32076 is 2916. Furthermore, 32076 divided by 2916 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 32076 in its simplest radical form as follows:

√32076 = A√B

√32076 = 54√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 32076 to simplify the square root of 32076 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 32076 and then take the square root of that product. The prime factors that multiply together to make 32076 are 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 11. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 = 2916 and the square root of 2916 is 54. Therefore, A equals 54.

B = Divide 32076 by the number (A) squared. 54 squared is 2916 and 32076 divided by 2916 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 32076 in its simplest radical form as follows:

√32076 = A√B

√32076 = 54√11

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