Simplify Square Root of 25168

Here we will show you two methods that you can use to simplify the square root of 25168. In other words, we will show you how to find the square root of 25168 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.

√25168 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 25168 to simplify the square root of 25168. 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 25168. The factors of 25168 are 1, 2, 4, 8, 11, 13, 16, 22, 26, 44, 52, 88, 104, 121, 143, 176, 208, 242, 286, 484, 572, 968, 1144, 1573, 1936, 2288, 3146, 6292, 12584, and 25168. Furthermore, the greatest perfect square on this list is 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Calculate 25168 divided by the greatest perfect square from the list of all factors of 25168. We determined above that the greatest perfect square from the list of all factors of 25168 is 1936. Furthermore, 25168 divided by 1936 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 25168 in its simplest radical form as follows:

√25168 = A√B

√25168 = 44√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 25168 to simplify the square root of 25168 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 25168 and then take the square root of that product. The prime factors that multiply together to make 25168 are 2 x 2 x 2 x 2 x 11 x 11 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 11 x 11 = 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Divide 25168 by the number (A) squared. 44 squared is 1936 and 25168 divided by 1936 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 25168 in its simplest radical form as follows:

√25168 = A√B

√25168 = 44√13

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