Simplify Square Root of 24420

Here we will show you two methods that you can use to simplify the square root of 24420. In other words, we will show you how to find the square root of 24420 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.

√24420 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 24420 to simplify the square root of 24420. 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 24420. The factors of 24420 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 37, 44, 55, 60, 66, 74, 110, 111, 132, 148, 165, 185, 220, 222, 330, 370, 407, 444, 555, 660, 740, 814, 1110, 1221, 1628, 2035, 2220, 2442, 4070, 4884, 6105, 8140, 12210, and 24420. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 24420 divided by the greatest perfect square from the list of all factors of 24420. We determined above that the greatest perfect square from the list of all factors of 24420 is 4. Furthermore, 24420 divided by 4 is 6105, therefore B equals 6105.

Now we have A and B and can get our answer to 24420 in its simplest radical form as follows:

√24420 = A√B

√24420 = 2√6105

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 24420 to simplify the square root of 24420 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 24420 and then take the square root of that product. The prime factors that multiply together to make 24420 are 2 x 2 x 3 x 5 x 11 x 37. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 24420 by the number (A) squared. 2 squared is 4 and 24420 divided by 4 is 6105. Therefore, B equals 6105.

Once again we have A and B and can get our answer to 24420 in its simplest radical form as follows:

√24420 = A√B

√24420 = 2√6105

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