Simplify Square Root of 33516

Here we will show you two methods that you can use to simplify the square root of 33516. In other words, we will show you how to find the square root of 33516 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.

√33516 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 33516 to simplify the square root of 33516. 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 33516. The factors of 33516 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 19, 21, 28, 36, 38, 42, 49, 57, 63, 76, 84, 98, 114, 126, 133, 147, 171, 196, 228, 252, 266, 294, 342, 399, 441, 532, 588, 684, 798, 882, 931, 1197, 1596, 1764, 1862, 2394, 2793, 3724, 4788, 5586, 8379, 11172, 16758, and 33516. Furthermore, the greatest perfect square on this list is 1764 and the square root of 1764 is 42. Therefore, A equals 42.

B = Calculate 33516 divided by the greatest perfect square from the list of all factors of 33516. We determined above that the greatest perfect square from the list of all factors of 33516 is 1764. Furthermore, 33516 divided by 1764 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 33516 in its simplest radical form as follows:

√33516 = A√B

√33516 = 42√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 33516 to simplify the square root of 33516 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 33516 and then take the square root of that product. The prime factors that multiply together to make 33516 are 2 x 2 x 3 x 3 x 7 x 7 x 19. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 7 x 7 = 1764 and the square root of 1764 is 42. Therefore, A equals 42.

B = Divide 33516 by the number (A) squared. 42 squared is 1764 and 33516 divided by 1764 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 33516 in its simplest radical form as follows:

√33516 = A√B

√33516 = 42√19

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