Simplify Square Root of 52822

Here we will show you two methods that you can use to simplify the square root of 52822. In other words, we will show you how to find the square root of 52822 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.

√52822 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52822 to simplify the square root of 52822. 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 52822. The factors of 52822 are 1, 2, 7, 11, 14, 22, 49, 77, 98, 154, 343, 539, 686, 1078, 2401, 3773, 4802, 7546, 26411, and 52822. Furthermore, the greatest perfect square on this list is 2401 and the square root of 2401 is 49. Therefore, A equals 49.

B = Calculate 52822 divided by the greatest perfect square from the list of all factors of 52822. We determined above that the greatest perfect square from the list of all factors of 52822 is 2401. Furthermore, 52822 divided by 2401 is 22, therefore B equals 22.

Now we have A and B and can get our answer to 52822 in its simplest radical form as follows:

√52822 = A√B

√52822 = 49√22

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52822 to simplify the square root of 52822 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 52822 and then take the square root of that product. The prime factors that multiply together to make 52822 are 2 x 7 x 7 x 7 x 7 x 11. When we strip out the pairs only, we get 7 x 7 x 7 x 7 = 2401 and the square root of 2401 is 49. Therefore, A equals 49.

B = Divide 52822 by the number (A) squared. 49 squared is 2401 and 52822 divided by 2401 is 22. Therefore, B equals 22.

Once again we have A and B and can get our answer to 52822 in its simplest radical form as follows:

√52822 = A√B

√52822 = 49√22

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Simplify Square Root of 52823
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