Simplify Square Root of 58800

Here we will show you two methods that you can use to simplify the square root of 58800. In other words, we will show you how to find the square root of 58800 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.

√58800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58800 to simplify the square root of 58800. 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 58800. The factors of 58800 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 49, 50, 56, 60, 70, 75, 80, 84, 98, 100, 105, 112, 120, 140, 147, 150, 168, 175, 196, 200, 210, 240, 245, 280, 294, 300, 336, 350, 392, 400, 420, 490, 525, 560, 588, 600, 700, 735, 784, 840, 980, 1050, 1176, 1200, 1225, 1400, 1470, 1680, 1960, 2100, 2352, 2450, 2800, 2940, 3675, 3920, 4200, 4900, 5880, 7350, 8400, 9800, 11760, 14700, 19600, 29400, and 58800. Furthermore, the greatest perfect square on this list is 19600 and the square root of 19600 is 140. Therefore, A equals 140.

B = Calculate 58800 divided by the greatest perfect square from the list of all factors of 58800. We determined above that the greatest perfect square from the list of all factors of 58800 is 19600. Furthermore, 58800 divided by 19600 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 58800 in its simplest radical form as follows:

√58800 = A√B

√58800 = 140√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58800 to simplify the square root of 58800 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 58800 and then take the square root of that product. The prime factors that multiply together to make 58800 are 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 5 x 5 x 7 x 7 = 19600 and the square root of 19600 is 140. Therefore, A equals 140.

B = Divide 58800 by the number (A) squared. 140 squared is 19600 and 58800 divided by 19600 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 58800 in its simplest radical form as follows:

√58800 = A√B

√58800 = 140√3

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Simplify Square Root of 58801
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