Simplify Square Root of 34344

Here we will show you two methods that you can use to simplify the square root of 34344. In other words, we will show you how to find the square root of 34344 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.

√34344 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34344 to simplify the square root of 34344. 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 34344. The factors of 34344 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 53, 54, 72, 81, 106, 108, 159, 162, 212, 216, 318, 324, 424, 477, 636, 648, 954, 1272, 1431, 1908, 2862, 3816, 4293, 5724, 8586, 11448, 17172, and 34344. Furthermore, the greatest perfect square on this list is 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Calculate 34344 divided by the greatest perfect square from the list of all factors of 34344. We determined above that the greatest perfect square from the list of all factors of 34344 is 324. Furthermore, 34344 divided by 324 is 106, therefore B equals 106.

Now we have A and B and can get our answer to 34344 in its simplest radical form as follows:

√34344 = A√B

√34344 = 18√106

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34344 to simplify the square root of 34344 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 34344 and then take the square root of that product. The prime factors that multiply together to make 34344 are 2 x 2 x 2 x 3 x 3 x 3 x 3 x 53. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 = 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Divide 34344 by the number (A) squared. 18 squared is 324 and 34344 divided by 324 is 106. Therefore, B equals 106.

Once again we have A and B and can get our answer to 34344 in its simplest radical form as follows:

√34344 = A√B

√34344 = 18√106

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