Simplify Square Root of 28812




Here we will show you two methods that you can use to simplify the square root of 28812. In other words, we will show you how to find the square root of 28812 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.

28812 = A√B




Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 28812 to simplify the square root of 28812. 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 28812. The factors of 28812 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 343, 588, 686, 1029, 1372, 2058, 2401, 4116, 4802, 7203, 9604, 14406, and 28812. Furthermore, the greatest perfect square on this list is 9604 and the square root of 9604 is 98. Therefore, A equals 98.

B = Calculate 28812 divided by the greatest perfect square from the list of all factors of 28812. We determined above that the greatest perfect square from the list of all factors of 28812 is 9604. Furthermore, 28812 divided by 9604 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 28812 in its simplest radical form as follows:

28812 = A√B

28812 = 98√3




Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 28812 to simplify the square root of 28812 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 28812 and then take the square root of that product. The prime factors that multiply together to make 28812 are 2 x 2 x 3 x 7 x 7 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 7 x 7 x 7 x 7 = 9604 and the square root of 9604 is 98. Therefore, A equals 98.

B = Divide 28812 by the number (A) squared. 98 squared is 9604 and 28812 divided by 9604 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 28812 in its simplest radical form as follows:

28812 = A√B

28812 = 98√3



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