Simplify Square Root of 36822

Here we will show you two methods that you can use to simplify the square root of 36822. In other words, we will show you how to find the square root of 36822 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.

√36822 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 36822 to simplify the square root of 36822. 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 36822. The factors of 36822 are 1, 2, 3, 6, 17, 19, 34, 38, 51, 57, 102, 114, 323, 361, 646, 722, 969, 1083, 1938, 2166, 6137, 12274, 18411, and 36822. Furthermore, the greatest perfect square on this list is 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Calculate 36822 divided by the greatest perfect square from the list of all factors of 36822. We determined above that the greatest perfect square from the list of all factors of 36822 is 361. Furthermore, 36822 divided by 361 is 102, therefore B equals 102.

Now we have A and B and can get our answer to 36822 in its simplest radical form as follows:

√36822 = A√B

√36822 = 19√102

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 36822 to simplify the square root of 36822 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 36822 and then take the square root of that product. The prime factors that multiply together to make 36822 are 2 x 3 x 17 x 19 x 19. When we strip out the pairs only, we get 19 x 19 = 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Divide 36822 by the number (A) squared. 19 squared is 361 and 36822 divided by 361 is 102. Therefore, B equals 102.

Once again we have A and B and can get our answer to 36822 in its simplest radical form as follows:

√36822 = A√B

√36822 = 19√102

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Simplify Square Root of 36823
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