Simplify Square Root of 3822

Here we will show you two methods that you can use to simplify the square root of 3822. In other words, we will show you how to find the square root of 3822 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.

√3822 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 3822 to simplify the square root of 3822. 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 3822. The factors of 3822 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 49, 78, 91, 98, 147, 182, 273, 294, 546, 637, 1274, 1911, and 3822. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 3822 divided by the greatest perfect square from the list of all factors of 3822. We determined above that the greatest perfect square from the list of all factors of 3822 is 49. Furthermore, 3822 divided by 49 is 78, therefore B equals 78.

Now we have A and B and can get our answer to 3822 in its simplest radical form as follows:

√3822 = A√B

√3822 = 7√78

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 3822 to simplify the square root of 3822 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 3822 and then take the square root of that product. The prime factors that multiply together to make 3822 are 2 x 3 x 7 x 7 x 13. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 3822 by the number (A) squared. 7 squared is 49 and 3822 divided by 49 is 78. Therefore, B equals 78.

Once again we have A and B and can get our answer to 3822 in its simplest radical form as follows:

√3822 = A√B

√3822 = 7√78

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

Simplify Square Root of 3823
Here is the next square root on our list that we have simplifed for you.