Simplify Square Root of 22188

Here we will show you two methods that you can use to simplify the square root of 22188. In other words, we will show you how to find the square root of 22188 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.

√22188 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22188 to simplify the square root of 22188. 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 22188. The factors of 22188 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516, 1849, 3698, 5547, 7396, 11094, and 22188. Furthermore, the greatest perfect square on this list is 7396 and the square root of 7396 is 86. Therefore, A equals 86.

B = Calculate 22188 divided by the greatest perfect square from the list of all factors of 22188. We determined above that the greatest perfect square from the list of all factors of 22188 is 7396. Furthermore, 22188 divided by 7396 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 22188 in its simplest radical form as follows:

√22188 = A√B

√22188 = 86√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22188 to simplify the square root of 22188 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 22188 and then take the square root of that product. The prime factors that multiply together to make 22188 are 2 x 2 x 3 x 43 x 43. When we strip out the pairs only, we get 2 x 2 x 43 x 43 = 7396 and the square root of 7396 is 86. Therefore, A equals 86.

B = Divide 22188 by the number (A) squared. 86 squared is 7396 and 22188 divided by 7396 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 22188 in its simplest radical form as follows:

√22188 = A√B

√22188 = 86√3

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Simplify Square Root of 22189
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