Simplify Square Root of 20184

Here we will show you two methods that you can use to simplify the square root of 20184. In other words, we will show you how to find the square root of 20184 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.

√20184 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 20184 to simplify the square root of 20184. 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 20184. The factors of 20184 are 1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696, 841, 1682, 2523, 3364, 5046, 6728, 10092, and 20184. Furthermore, the greatest perfect square on this list is 3364 and the square root of 3364 is 58. Therefore, A equals 58.

B = Calculate 20184 divided by the greatest perfect square from the list of all factors of 20184. We determined above that the greatest perfect square from the list of all factors of 20184 is 3364. Furthermore, 20184 divided by 3364 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 20184 in its simplest radical form as follows:

√20184 = A√B

√20184 = 58√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 20184 to simplify the square root of 20184 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 20184 and then take the square root of that product. The prime factors that multiply together to make 20184 are 2 x 2 x 2 x 3 x 29 x 29. When we strip out the pairs only, we get 2 x 2 x 29 x 29 = 3364 and the square root of 3364 is 58. Therefore, A equals 58.

B = Divide 20184 by the number (A) squared. 58 squared is 3364 and 20184 divided by 3364 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 20184 in its simplest radical form as follows:

√20184 = A√B

√20184 = 58√6

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Simplify Square Root of 20185
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