Simplify Square Root of 21780

Here we will show you two methods that you can use to simplify the square root of 21780. In other words, we will show you how to find the square root of 21780 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.

√21780 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 21780 to simplify the square root of 21780. 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 21780. The factors of 21780 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 121, 132, 165, 180, 198, 220, 242, 330, 363, 396, 484, 495, 605, 660, 726, 990, 1089, 1210, 1452, 1815, 1980, 2178, 2420, 3630, 4356, 5445, 7260, 10890, and 21780. Furthermore, the greatest perfect square on this list is 4356 and the square root of 4356 is 66. Therefore, A equals 66.

B = Calculate 21780 divided by the greatest perfect square from the list of all factors of 21780. We determined above that the greatest perfect square from the list of all factors of 21780 is 4356. Furthermore, 21780 divided by 4356 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 21780 in its simplest radical form as follows:

√21780 = A√B

√21780 = 66√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 21780 to simplify the square root of 21780 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 21780 and then take the square root of that product. The prime factors that multiply together to make 21780 are 2 x 2 x 3 x 3 x 5 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 11 x 11 = 4356 and the square root of 4356 is 66. Therefore, A equals 66.

B = Divide 21780 by the number (A) squared. 66 squared is 4356 and 21780 divided by 4356 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 21780 in its simplest radical form as follows:

√21780 = A√B

√21780 = 66√5

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Simplify Square Root of 21781
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