Simplify Square Root of 22812

Here we will show you two methods that you can use to simplify the square root of 22812. In other words, we will show you how to find the square root of 22812 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.

√22812 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22812 to simplify the square root of 22812. 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 22812. The factors of 22812 are 1, 2, 3, 4, 6, 12, 1901, 3802, 5703, 7604, 11406, and 22812. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 22812 divided by the greatest perfect square from the list of all factors of 22812. We determined above that the greatest perfect square from the list of all factors of 22812 is 4. Furthermore, 22812 divided by 4 is 5703, therefore B equals 5703.

Now we have A and B and can get our answer to 22812 in its simplest radical form as follows:

√22812 = A√B

√22812 = 2√5703

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22812 to simplify the square root of 22812 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 22812 and then take the square root of that product. The prime factors that multiply together to make 22812 are 2 x 2 x 3 x 1901. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 22812 by the number (A) squared. 2 squared is 4 and 22812 divided by 4 is 5703. Therefore, B equals 5703.

Once again we have A and B and can get our answer to 22812 in its simplest radical form as follows:

√22812 = A√B

√22812 = 2√5703

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Simplify Square Root of 22813
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