Simplify Square Root of 18876

Here we will show you two methods that you can use to simplify the square root of 18876. In other words, we will show you how to find the square root of 18876 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.

√18876 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18876 to simplify the square root of 18876. 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 18876. The factors of 18876 are 1, 2, 3, 4, 6, 11, 12, 13, 22, 26, 33, 39, 44, 52, 66, 78, 121, 132, 143, 156, 242, 286, 363, 429, 484, 572, 726, 858, 1452, 1573, 1716, 3146, 4719, 6292, 9438, and 18876. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 18876 divided by the greatest perfect square from the list of all factors of 18876. We determined above that the greatest perfect square from the list of all factors of 18876 is 484. Furthermore, 18876 divided by 484 is 39, therefore B equals 39.

Now we have A and B and can get our answer to 18876 in its simplest radical form as follows:

√18876 = A√B

√18876 = 22√39

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18876 to simplify the square root of 18876 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 18876 and then take the square root of that product. The prime factors that multiply together to make 18876 are 2 x 2 x 3 x 11 x 11 x 13. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 18876 by the number (A) squared. 22 squared is 484 and 18876 divided by 484 is 39. Therefore, B equals 39.

Once again we have A and B and can get our answer to 18876 in its simplest radical form as follows:

√18876 = A√B

√18876 = 22√39

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