Simplify Square Root of 52920

Here we will show you two methods that you can use to simplify the square root of 52920. In other words, we will show you how to find the square root of 52920 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.

√52920 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52920 to simplify the square root of 52920. 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 52920. The factors of 52920 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 49, 54, 56, 60, 63, 70, 72, 84, 90, 98, 105, 108, 120, 126, 135, 140, 147, 168, 180, 189, 196, 210, 216, 245, 252, 270, 280, 294, 315, 360, 378, 392, 420, 441, 490, 504, 540, 588, 630, 735, 756, 840, 882, 945, 980, 1080, 1176, 1260, 1323, 1470, 1512, 1764, 1890, 1960, 2205, 2520, 2646, 2940, 3528, 3780, 4410, 5292, 5880, 6615, 7560, 8820, 10584, 13230, 17640, 26460, and 52920. Furthermore, the greatest perfect square on this list is 1764 and the square root of 1764 is 42. Therefore, A equals 42.

B = Calculate 52920 divided by the greatest perfect square from the list of all factors of 52920. We determined above that the greatest perfect square from the list of all factors of 52920 is 1764. Furthermore, 52920 divided by 1764 is 30, therefore B equals 30.

Now we have A and B and can get our answer to 52920 in its simplest radical form as follows:

√52920 = A√B

√52920 = 42√30

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52920 to simplify the square root of 52920 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 52920 and then take the square root of that product. The prime factors that multiply together to make 52920 are 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 7 x 7 = 1764 and the square root of 1764 is 42. Therefore, A equals 42.

B = Divide 52920 by the number (A) squared. 42 squared is 1764 and 52920 divided by 1764 is 30. Therefore, B equals 30.

Once again we have A and B and can get our answer to 52920 in its simplest radical form as follows:

√52920 = A√B

√52920 = 42√30

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Simplify Square Root of 52921
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