Simplify Square Root of 22680

Here we will show you two methods that you can use to simplify the square root of 22680. In other words, we will show you how to find the square root of 22680 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.

√22680 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22680 to simplify the square root of 22680. 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 22680. The factors of 22680 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 54, 56, 60, 63, 70, 72, 81, 84, 90, 105, 108, 120, 126, 135, 140, 162, 168, 180, 189, 210, 216, 252, 270, 280, 315, 324, 360, 378, 405, 420, 504, 540, 567, 630, 648, 756, 810, 840, 945, 1080, 1134, 1260, 1512, 1620, 1890, 2268, 2520, 2835, 3240, 3780, 4536, 5670, 7560, 11340, and 22680. Furthermore, the greatest perfect square on this list is 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Calculate 22680 divided by the greatest perfect square from the list of all factors of 22680. We determined above that the greatest perfect square from the list of all factors of 22680 is 324. Furthermore, 22680 divided by 324 is 70, therefore B equals 70.

Now we have A and B and can get our answer to 22680 in its simplest radical form as follows:

√22680 = A√B

√22680 = 18√70

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22680 to simplify the square root of 22680 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 22680 and then take the square root of that product. The prime factors that multiply together to make 22680 are 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 = 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Divide 22680 by the number (A) squared. 18 squared is 324 and 22680 divided by 324 is 70. Therefore, B equals 70.

Once again we have A and B and can get our answer to 22680 in its simplest radical form as follows:

√22680 = A√B

√22680 = 18√70

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