Simplify Square Root of 33708

Here we will show you two methods that you can use to simplify the square root of 33708. In other words, we will show you how to find the square root of 33708 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.

√33708 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 33708 to simplify the square root of 33708. 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 33708. The factors of 33708 are 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636, 2809, 5618, 8427, 11236, 16854, and 33708. Furthermore, the greatest perfect square on this list is 11236 and the square root of 11236 is 106. Therefore, A equals 106.

B = Calculate 33708 divided by the greatest perfect square from the list of all factors of 33708. We determined above that the greatest perfect square from the list of all factors of 33708 is 11236. Furthermore, 33708 divided by 11236 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 33708 in its simplest radical form as follows:

√33708 = A√B

√33708 = 106√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 33708 to simplify the square root of 33708 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 33708 and then take the square root of that product. The prime factors that multiply together to make 33708 are 2 x 2 x 3 x 53 x 53. When we strip out the pairs only, we get 2 x 2 x 53 x 53 = 11236 and the square root of 11236 is 106. Therefore, A equals 106.

B = Divide 33708 by the number (A) squared. 106 squared is 11236 and 33708 divided by 11236 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 33708 in its simplest radical form as follows:

√33708 = A√B

√33708 = 106√3

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Simplify Square Root of 33709
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