Simplify Square Root of 89100

Here we will show you two methods that you can use to simplify the square root of 89100. In other words, we will show you how to find the square root of 89100 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.

√89100 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89100 to simplify the square root of 89100. 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 89100. The factors of 89100 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 27, 30, 33, 36, 44, 45, 50, 54, 55, 60, 66, 75, 81, 90, 99, 100, 108, 110, 132, 135, 150, 162, 165, 180, 198, 220, 225, 270, 275, 297, 300, 324, 330, 396, 405, 450, 495, 540, 550, 594, 660, 675, 810, 825, 891, 900, 990, 1100, 1188, 1350, 1485, 1620, 1650, 1782, 1980, 2025, 2475, 2700, 2970, 3300, 3564, 4050, 4455, 4950, 5940, 7425, 8100, 8910, 9900, 14850, 17820, 22275, 29700, 44550, and 89100. Furthermore, the greatest perfect square on this list is 8100 and the square root of 8100 is 90. Therefore, A equals 90.

B = Calculate 89100 divided by the greatest perfect square from the list of all factors of 89100. We determined above that the greatest perfect square from the list of all factors of 89100 is 8100. Furthermore, 89100 divided by 8100 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 89100 in its simplest radical form as follows:

√89100 = A√B

√89100 = 90√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89100 to simplify the square root of 89100 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 89100 and then take the square root of that product. The prime factors that multiply together to make 89100 are 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 x 11. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 = 8100 and the square root of 8100 is 90. Therefore, A equals 90.

B = Divide 89100 by the number (A) squared. 90 squared is 8100 and 89100 divided by 8100 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 89100 in its simplest radical form as follows:

√89100 = A√B

√89100 = 90√11

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