Simplify Square Root of 88200

Here we will show you two methods that you can use to simplify the square root of 88200. In other words, we will show you how to find the square root of 88200 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.

√88200 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88200 to simplify the square root of 88200. 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 88200. The factors of 88200 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 49, 50, 56, 60, 63, 70, 72, 75, 84, 90, 98, 100, 105, 120, 126, 140, 147, 150, 168, 175, 180, 196, 200, 210, 225, 245, 252, 280, 294, 300, 315, 350, 360, 392, 420, 441, 450, 490, 504, 525, 588, 600, 630, 700, 735, 840, 882, 900, 980, 1050, 1176, 1225, 1260, 1400, 1470, 1575, 1764, 1800, 1960, 2100, 2205, 2450, 2520, 2940, 3150, 3528, 3675, 4200, 4410, 4900, 5880, 6300, 7350, 8820, 9800, 11025, 12600, 14700, 17640, 22050, 29400, 44100, and 88200. Furthermore, the greatest perfect square on this list is 44100 and the square root of 44100 is 210. Therefore, A equals 210.

B = Calculate 88200 divided by the greatest perfect square from the list of all factors of 88200. We determined above that the greatest perfect square from the list of all factors of 88200 is 44100. Furthermore, 88200 divided by 44100 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 88200 in its simplest radical form as follows:

√88200 = A√B

√88200 = 210√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88200 to simplify the square root of 88200 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 88200 and then take the square root of that product. The prime factors that multiply together to make 88200 are 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 5 x 5 x 7 x 7 = 44100 and the square root of 44100 is 210. Therefore, A equals 210.

B = Divide 88200 by the number (A) squared. 210 squared is 44100 and 88200 divided by 44100 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 88200 in its simplest radical form as follows:

√88200 = A√B

√88200 = 210√2

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Simplify Square Root of 88201
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