Simplify Square Root of 10808

Here we will show you two methods that you can use to simplify the square root of 10808. In other words, we will show you how to find the square root of 10808 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.

√10808 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10808 to simplify the square root of 10808. 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 10808. The factors of 10808 are 1, 2, 4, 7, 8, 14, 28, 56, 193, 386, 772, 1351, 1544, 2702, 5404, and 10808. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 10808 divided by the greatest perfect square from the list of all factors of 10808. We determined above that the greatest perfect square from the list of all factors of 10808 is 4. Furthermore, 10808 divided by 4 is 2702, therefore B equals 2702.

Now we have A and B and can get our answer to 10808 in its simplest radical form as follows:

√10808 = A√B

√10808 = 2√2702

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10808 to simplify the square root of 10808 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 10808 and then take the square root of that product. The prime factors that multiply together to make 10808 are 2 x 2 x 2 x 7 x 193. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 10808 by the number (A) squared. 2 squared is 4 and 10808 divided by 4 is 2702. Therefore, B equals 2702.

Once again we have A and B and can get our answer to 10808 in its simplest radical form as follows:

√10808 = A√B

√10808 = 2√2702

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Simplify Square Root of 10809
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