Simplify Square Root of 24696

Here we will show you two methods that you can use to simplify the square root of 24696. In other words, we will show you how to find the square root of 24696 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.

√24696 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 24696 to simplify the square root of 24696. 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 24696. The factors of 24696 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 343, 392, 441, 504, 588, 686, 882, 1029, 1176, 1372, 1764, 2058, 2744, 3087, 3528, 4116, 6174, 8232, 12348, and 24696. Furthermore, the greatest perfect square on this list is 1764 and the square root of 1764 is 42. Therefore, A equals 42.

B = Calculate 24696 divided by the greatest perfect square from the list of all factors of 24696. We determined above that the greatest perfect square from the list of all factors of 24696 is 1764. Furthermore, 24696 divided by 1764 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 24696 in its simplest radical form as follows:

√24696 = A√B

√24696 = 42√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 24696 to simplify the square root of 24696 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 24696 and then take the square root of that product. The prime factors that multiply together to make 24696 are 2 x 2 x 2 x 3 x 3 x 7 x 7 x 7. 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 24696 by the number (A) squared. 42 squared is 1764 and 24696 divided by 1764 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 24696 in its simplest radical form as follows:

√24696 = A√B

√24696 = 42√14

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