Simplify Square Root of 34104

Here we will show you two methods that you can use to simplify the square root of 34104. In other words, we will show you how to find the square root of 34104 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.

√34104 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34104 to simplify the square root of 34104. 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 34104. The factors of 34104 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 29, 42, 49, 56, 58, 84, 87, 98, 116, 147, 168, 174, 196, 203, 232, 294, 348, 392, 406, 588, 609, 696, 812, 1176, 1218, 1421, 1624, 2436, 2842, 4263, 4872, 5684, 8526, 11368, 17052, and 34104. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 34104 divided by the greatest perfect square from the list of all factors of 34104. We determined above that the greatest perfect square from the list of all factors of 34104 is 196. Furthermore, 34104 divided by 196 is 174, therefore B equals 174.

Now we have A and B and can get our answer to 34104 in its simplest radical form as follows:

√34104 = A√B

√34104 = 14√174

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34104 to simplify the square root of 34104 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 34104 and then take the square root of that product. The prime factors that multiply together to make 34104 are 2 x 2 x 2 x 3 x 7 x 7 x 29. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 34104 by the number (A) squared. 14 squared is 196 and 34104 divided by 196 is 174. Therefore, B equals 174.

Once again we have A and B and can get our answer to 34104 in its simplest radical form as follows:

√34104 = A√B

√34104 = 14√174

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