Simplify Square Root of 23520

Here we will show you two methods that you can use to simplify the square root of 23520. In other words, we will show you how to find the square root of 23520 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.

√23520 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23520 to simplify the square root of 23520. 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 23520. The factors of 23520 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 96, 98, 105, 112, 120, 140, 147, 160, 168, 196, 210, 224, 240, 245, 280, 294, 336, 392, 420, 480, 490, 560, 588, 672, 735, 784, 840, 980, 1120, 1176, 1470, 1568, 1680, 1960, 2352, 2940, 3360, 3920, 4704, 5880, 7840, 11760, and 23520. Furthermore, the greatest perfect square on this list is 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Calculate 23520 divided by the greatest perfect square from the list of all factors of 23520. We determined above that the greatest perfect square from the list of all factors of 23520 is 784. Furthermore, 23520 divided by 784 is 30, therefore B equals 30.

Now we have A and B and can get our answer to 23520 in its simplest radical form as follows:

√23520 = A√B

√23520 = 28√30

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23520 to simplify the square root of 23520 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 23520 and then take the square root of that product. The prime factors that multiply together to make 23520 are 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 7 x 7 = 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Divide 23520 by the number (A) squared. 28 squared is 784 and 23520 divided by 784 is 30. Therefore, B equals 30.

Once again we have A and B and can get our answer to 23520 in its simplest radical form as follows:

√23520 = A√B

√23520 = 28√30

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