Simplify Square Root of 72720

Here we will show you two methods that you can use to simplify the square root of 72720. In other words, we will show you how to find the square root of 72720 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.

√72720 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72720 to simplify the square root of 72720. 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 72720. The factors of 72720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 101, 120, 144, 180, 202, 240, 303, 360, 404, 505, 606, 720, 808, 909, 1010, 1212, 1515, 1616, 1818, 2020, 2424, 3030, 3636, 4040, 4545, 4848, 6060, 7272, 8080, 9090, 12120, 14544, 18180, 24240, 36360, and 72720. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 72720 divided by the greatest perfect square from the list of all factors of 72720. We determined above that the greatest perfect square from the list of all factors of 72720 is 144. Furthermore, 72720 divided by 144 is 505, therefore B equals 505.

Now we have A and B and can get our answer to 72720 in its simplest radical form as follows:

√72720 = A√B

√72720 = 12√505

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72720 to simplify the square root of 72720 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 72720 and then take the square root of that product. The prime factors that multiply together to make 72720 are 2 x 2 x 2 x 2 x 3 x 3 x 5 x 101. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 72720 by the number (A) squared. 12 squared is 144 and 72720 divided by 144 is 505. Therefore, B equals 505.

Once again we have A and B and can get our answer to 72720 in its simplest radical form as follows:

√72720 = A√B

√72720 = 12√505

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Simplify Square Root of 72721
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