Simplify Square Root of 34848

Here we will show you two methods that you can use to simplify the square root of 34848. In other words, we will show you how to find the square root of 34848 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.

√34848 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34848 to simplify the square root of 34848. 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 34848. The factors of 34848 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36, 44, 48, 66, 72, 88, 96, 99, 121, 132, 144, 176, 198, 242, 264, 288, 352, 363, 396, 484, 528, 726, 792, 968, 1056, 1089, 1452, 1584, 1936, 2178, 2904, 3168, 3872, 4356, 5808, 8712, 11616, 17424, and 34848. Furthermore, the greatest perfect square on this list is 17424 and the square root of 17424 is 132. Therefore, A equals 132.

B = Calculate 34848 divided by the greatest perfect square from the list of all factors of 34848. We determined above that the greatest perfect square from the list of all factors of 34848 is 17424. Furthermore, 34848 divided by 17424 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 34848 in its simplest radical form as follows:

√34848 = A√B

√34848 = 132√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34848 to simplify the square root of 34848 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 34848 and then take the square root of that product. The prime factors that multiply together to make 34848 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 11 x 11 = 17424 and the square root of 17424 is 132. Therefore, A equals 132.

B = Divide 34848 by the number (A) squared. 132 squared is 17424 and 34848 divided by 17424 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 34848 in its simplest radical form as follows:

√34848 = A√B

√34848 = 132√2

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