Simplify Square Root of 24926

Here we will show you two methods that you can use to simplify the square root of 24926. In other words, we will show you how to find the square root of 24926 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.

√24926 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 24926 to simplify the square root of 24926. 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 24926. The factors of 24926 are 1, 2, 11, 22, 103, 121, 206, 242, 1133, 2266, 12463, and 24926. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 24926 divided by the greatest perfect square from the list of all factors of 24926. We determined above that the greatest perfect square from the list of all factors of 24926 is 121. Furthermore, 24926 divided by 121 is 206, therefore B equals 206.

Now we have A and B and can get our answer to 24926 in its simplest radical form as follows:

√24926 = A√B

√24926 = 11√206

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 24926 to simplify the square root of 24926 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 24926 and then take the square root of that product. The prime factors that multiply together to make 24926 are 2 x 11 x 11 x 103. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 24926 by the number (A) squared. 11 squared is 121 and 24926 divided by 121 is 206. Therefore, B equals 206.

Once again we have A and B and can get our answer to 24926 in its simplest radical form as follows:

√24926 = A√B

√24926 = 11√206

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Simplify Square Root of 24927
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