Simplify Square Root of 2812

Here we will show you two methods that you can use to simplify the square root of 2812. In other words, we will show you how to find the square root of 2812 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.

√2812 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2812 to simplify the square root of 2812. 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 2812. The factors of 2812 are 1, 2, 4, 19, 37, 38, 74, 76, 148, 703, 1406, and 2812. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 2812 divided by the greatest perfect square from the list of all factors of 2812. We determined above that the greatest perfect square from the list of all factors of 2812 is 4. Furthermore, 2812 divided by 4 is 703, therefore B equals 703.

Now we have A and B and can get our answer to 2812 in its simplest radical form as follows:

√2812 = A√B

√2812 = 2√703

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2812 to simplify the square root of 2812 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 2812 and then take the square root of that product. The prime factors that multiply together to make 2812 are 2 x 2 x 19 x 37. 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 2812 by the number (A) squared. 2 squared is 4 and 2812 divided by 4 is 703. Therefore, B equals 703.

Once again we have A and B and can get our answer to 2812 in its simplest radical form as follows:

√2812 = A√B

√2812 = 2√703

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 2813
Here is the next square root on our list that we have simplifed for you.