Simplify Square Root of 13320

Here we will show you two methods that you can use to simplify the square root of 13320. In other words, we will show you how to find the square root of 13320 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.

√13320 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 13320 to simplify the square root of 13320. 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 13320. The factors of 13320 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 37, 40, 45, 60, 72, 74, 90, 111, 120, 148, 180, 185, 222, 296, 333, 360, 370, 444, 555, 666, 740, 888, 1110, 1332, 1480, 1665, 2220, 2664, 3330, 4440, 6660, and 13320. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 13320 divided by the greatest perfect square from the list of all factors of 13320. We determined above that the greatest perfect square from the list of all factors of 13320 is 36. Furthermore, 13320 divided by 36 is 370, therefore B equals 370.

Now we have A and B and can get our answer to 13320 in its simplest radical form as follows:

√13320 = A√B

√13320 = 6√370

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 13320 to simplify the square root of 13320 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 13320 and then take the square root of that product. The prime factors that multiply together to make 13320 are 2 x 2 x 2 x 3 x 3 x 5 x 37. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 13320 by the number (A) squared. 6 squared is 36 and 13320 divided by 36 is 370. Therefore, B equals 370.

Once again we have A and B and can get our answer to 13320 in its simplest radical form as follows:

√13320 = A√B

√13320 = 6√370

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