Simplify Square Root of 20886

Here we will show you two methods that you can use to simplify the square root of 20886. In other words, we will show you how to find the square root of 20886 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.

√20886 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 20886 to simplify the square root of 20886. 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 20886. The factors of 20886 are 1, 2, 3, 6, 59, 118, 177, 354, 3481, 6962, 10443, and 20886. Furthermore, the greatest perfect square on this list is 3481 and the square root of 3481 is 59. Therefore, A equals 59.

B = Calculate 20886 divided by the greatest perfect square from the list of all factors of 20886. We determined above that the greatest perfect square from the list of all factors of 20886 is 3481. Furthermore, 20886 divided by 3481 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 20886 in its simplest radical form as follows:

√20886 = A√B

√20886 = 59√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 20886 to simplify the square root of 20886 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 20886 and then take the square root of that product. The prime factors that multiply together to make 20886 are 2 x 3 x 59 x 59. When we strip out the pairs only, we get 59 x 59 = 3481 and the square root of 3481 is 59. Therefore, A equals 59.

B = Divide 20886 by the number (A) squared. 59 squared is 3481 and 20886 divided by 3481 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 20886 in its simplest radical form as follows:

√20886 = A√B

√20886 = 59√6

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Simplify Square Root of 20887
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