Simplify Square Root of 16920

Here we will show you two methods that you can use to simplify the square root of 16920. In other words, we will show you how to find the square root of 16920 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.

√16920 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 16920 to simplify the square root of 16920. 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 16920. The factors of 16920 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 47, 60, 72, 90, 94, 120, 141, 180, 188, 235, 282, 360, 376, 423, 470, 564, 705, 846, 940, 1128, 1410, 1692, 1880, 2115, 2820, 3384, 4230, 5640, 8460, and 16920. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 16920 divided by the greatest perfect square from the list of all factors of 16920. We determined above that the greatest perfect square from the list of all factors of 16920 is 36. Furthermore, 16920 divided by 36 is 470, therefore B equals 470.

Now we have A and B and can get our answer to 16920 in its simplest radical form as follows:

√16920 = A√B

√16920 = 6√470

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 16920 to simplify the square root of 16920 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 16920 and then take the square root of that product. The prime factors that multiply together to make 16920 are 2 x 2 x 2 x 3 x 3 x 5 x 47. 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 16920 by the number (A) squared. 6 squared is 36 and 16920 divided by 36 is 470. Therefore, B equals 470.

Once again we have A and B and can get our answer to 16920 in its simplest radical form as follows:

√16920 = A√B

√16920 = 6√470

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