Simplify Square Root of 10108

Here we will show you two methods that you can use to simplify the square root of 10108. In other words, we will show you how to find the square root of 10108 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.

√10108 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10108 to simplify the square root of 10108. 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 10108. The factors of 10108 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 361, 532, 722, 1444, 2527, 5054, and 10108. Furthermore, the greatest perfect square on this list is 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Calculate 10108 divided by the greatest perfect square from the list of all factors of 10108. We determined above that the greatest perfect square from the list of all factors of 10108 is 1444. Furthermore, 10108 divided by 1444 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 10108 in its simplest radical form as follows:

√10108 = A√B

√10108 = 38√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10108 to simplify the square root of 10108 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 10108 and then take the square root of that product. The prime factors that multiply together to make 10108 are 2 x 2 x 7 x 19 x 19. When we strip out the pairs only, we get 2 x 2 x 19 x 19 = 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Divide 10108 by the number (A) squared. 38 squared is 1444 and 10108 divided by 1444 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 10108 in its simplest radical form as follows:

√10108 = A√B

√10108 = 38√7

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Simplify Square Root of 10109
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