Simplify Square Root of 60480

Here we will show you two methods that you can use to simplify the square root of 60480. In other words, we will show you how to find the square root of 60480 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.

√60480 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60480 to simplify the square root of 60480. 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 60480. The factors of 60480 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 108, 112, 120, 126, 135, 140, 144, 160, 168, 180, 189, 192, 210, 216, 224, 240, 252, 270, 280, 288, 315, 320, 336, 360, 378, 420, 432, 448, 480, 504, 540, 560, 576, 630, 672, 720, 756, 840, 864, 945, 960, 1008, 1080, 1120, 1260, 1344, 1440, 1512, 1680, 1728, 1890, 2016, 2160, 2240, 2520, 2880, 3024, 3360, 3780, 4032, 4320, 5040, 6048, 6720, 7560, 8640, 10080, 12096, 15120, 20160, 30240, and 60480. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 60480 divided by the greatest perfect square from the list of all factors of 60480. We determined above that the greatest perfect square from the list of all factors of 60480 is 576. Furthermore, 60480 divided by 576 is 105, therefore B equals 105.

Now we have A and B and can get our answer to 60480 in its simplest radical form as follows:

√60480 = A√B

√60480 = 24√105

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60480 to simplify the square root of 60480 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 60480 and then take the square root of that product. The prime factors that multiply together to make 60480 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 60480 by the number (A) squared. 24 squared is 576 and 60480 divided by 576 is 105. Therefore, B equals 105.

Once again we have A and B and can get our answer to 60480 in its simplest radical form as follows:

√60480 = A√B

√60480 = 24√105

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Simplify Square Root of 60481
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