Simplify Square Root of 91238

Here we will show you two methods that you can use to simplify the square root of 91238. In other words, we will show you how to find the square root of 91238 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.

√91238 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 91238 to simplify the square root of 91238. 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 91238. The factors of 91238 are 1, 2, 7, 14, 19, 38, 49, 98, 133, 266, 343, 686, 931, 1862, 2401, 4802, 6517, 13034, 45619, and 91238. Furthermore, the greatest perfect square on this list is 2401 and the square root of 2401 is 49. Therefore, A equals 49.

B = Calculate 91238 divided by the greatest perfect square from the list of all factors of 91238. We determined above that the greatest perfect square from the list of all factors of 91238 is 2401. Furthermore, 91238 divided by 2401 is 38, therefore B equals 38.

Now we have A and B and can get our answer to 91238 in its simplest radical form as follows:

√91238 = A√B

√91238 = 49√38

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 91238 to simplify the square root of 91238 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 91238 and then take the square root of that product. The prime factors that multiply together to make 91238 are 2 x 7 x 7 x 7 x 7 x 19. When we strip out the pairs only, we get 7 x 7 x 7 x 7 = 2401 and the square root of 2401 is 49. Therefore, A equals 49.

B = Divide 91238 by the number (A) squared. 49 squared is 2401 and 91238 divided by 2401 is 38. Therefore, B equals 38.

Once again we have A and B and can get our answer to 91238 in its simplest radical form as follows:

√91238 = A√B

√91238 = 49√38

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