Simplify Square Root of 26264

Here we will show you two methods that you can use to simplify the square root of 26264. In other words, we will show you how to find the square root of 26264 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.

√26264 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 26264 to simplify the square root of 26264. 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 26264. The factors of 26264 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 67, 98, 134, 196, 268, 392, 469, 536, 938, 1876, 3283, 3752, 6566, 13132, and 26264. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 26264 divided by the greatest perfect square from the list of all factors of 26264. We determined above that the greatest perfect square from the list of all factors of 26264 is 196. Furthermore, 26264 divided by 196 is 134, therefore B equals 134.

Now we have A and B and can get our answer to 26264 in its simplest radical form as follows:

√26264 = A√B

√26264 = 14√134

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 26264 to simplify the square root of 26264 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 26264 and then take the square root of that product. The prime factors that multiply together to make 26264 are 2 x 2 x 2 x 7 x 7 x 67. 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 26264 by the number (A) squared. 14 squared is 196 and 26264 divided by 196 is 134. Therefore, B equals 134.

Once again we have A and B and can get our answer to 26264 in its simplest radical form as follows:

√26264 = A√B

√26264 = 14√134

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Simplify Square Root of 26265
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