Simplify Square Root of 40224

Here we will show you two methods that you can use to simplify the square root of 40224. In other words, we will show you how to find the square root of 40224 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.

√40224 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40224 to simplify the square root of 40224. 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 40224. The factors of 40224 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 419, 838, 1257, 1676, 2514, 3352, 5028, 6704, 10056, 13408, 20112, and 40224. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 40224 divided by the greatest perfect square from the list of all factors of 40224. We determined above that the greatest perfect square from the list of all factors of 40224 is 16. Furthermore, 40224 divided by 16 is 2514, therefore B equals 2514.

Now we have A and B and can get our answer to 40224 in its simplest radical form as follows:

√40224 = A√B

√40224 = 4√2514

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40224 to simplify the square root of 40224 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 40224 and then take the square root of that product. The prime factors that multiply together to make 40224 are 2 x 2 x 2 x 2 x 2 x 3 x 419. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 40224 by the number (A) squared. 4 squared is 16 and 40224 divided by 16 is 2514. Therefore, B equals 2514.

Once again we have A and B and can get our answer to 40224 in its simplest radical form as follows:

√40224 = A√B

√40224 = 4√2514

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Simplify Square Root of 40225
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