Simplify Square Root of 52812

Here we will show you two methods that you can use to simplify the square root of 52812. In other words, we will show you how to find the square root of 52812 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.

√52812 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52812 to simplify the square root of 52812. 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 52812. The factors of 52812 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 163, 324, 326, 489, 652, 978, 1467, 1956, 2934, 4401, 5868, 8802, 13203, 17604, 26406, and 52812. Furthermore, the greatest perfect square on this list is 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Calculate 52812 divided by the greatest perfect square from the list of all factors of 52812. We determined above that the greatest perfect square from the list of all factors of 52812 is 324. Furthermore, 52812 divided by 324 is 163, therefore B equals 163.

Now we have A and B and can get our answer to 52812 in its simplest radical form as follows:

√52812 = A√B

√52812 = 18√163

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52812 to simplify the square root of 52812 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 52812 and then take the square root of that product. The prime factors that multiply together to make 52812 are 2 x 2 x 3 x 3 x 3 x 3 x 163. 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 52812 by the number (A) squared. 18 squared is 324 and 52812 divided by 324 is 163. Therefore, B equals 163.

Once again we have A and B and can get our answer to 52812 in its simplest radical form as follows:

√52812 = A√B

√52812 = 18√163

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