Simplify Square Root of 24300

Here we will show you two methods that you can use to simplify the square root of 24300. In other words, we will show you how to find the square root of 24300 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.

√24300 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 24300 to simplify the square root of 24300. 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 24300. The factors of 24300 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 81, 90, 100, 108, 135, 150, 162, 180, 225, 243, 270, 300, 324, 405, 450, 486, 540, 675, 810, 900, 972, 1215, 1350, 1620, 2025, 2430, 2700, 4050, 4860, 6075, 8100, 12150, and 24300. Furthermore, the greatest perfect square on this list is 8100 and the square root of 8100 is 90. Therefore, A equals 90.

B = Calculate 24300 divided by the greatest perfect square from the list of all factors of 24300. We determined above that the greatest perfect square from the list of all factors of 24300 is 8100. Furthermore, 24300 divided by 8100 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 24300 in its simplest radical form as follows:

√24300 = A√B

√24300 = 90√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 24300 to simplify the square root of 24300 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 24300 and then take the square root of that product. The prime factors that multiply together to make 24300 are 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 5. 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 24300 by the number (A) squared. 90 squared is 8100 and 24300 divided by 8100 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 24300 in its simplest radical form as follows:

√24300 = A√B

√24300 = 90√3

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Simplify Square Root of 24301
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