Simplify Square Root of 26852

Here we will show you two methods that you can use to simplify the square root of 26852. In other words, we will show you how to find the square root of 26852 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.

√26852 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 26852 to simplify the square root of 26852. 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 26852. The factors of 26852 are 1, 2, 4, 7, 14, 28, 49, 98, 137, 196, 274, 548, 959, 1918, 3836, 6713, 13426, and 26852. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 26852 divided by the greatest perfect square from the list of all factors of 26852. We determined above that the greatest perfect square from the list of all factors of 26852 is 196. Furthermore, 26852 divided by 196 is 137, therefore B equals 137.

Now we have A and B and can get our answer to 26852 in its simplest radical form as follows:

√26852 = A√B

√26852 = 14√137

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 26852 to simplify the square root of 26852 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 26852 and then take the square root of that product. The prime factors that multiply together to make 26852 are 2 x 2 x 7 x 7 x 137. 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 26852 by the number (A) squared. 14 squared is 196 and 26852 divided by 196 is 137. Therefore, B equals 137.

Once again we have A and B and can get our answer to 26852 in its simplest radical form as follows:

√26852 = A√B

√26852 = 14√137

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Simplify Square Root of 26853
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