Simplify Square Root of 43632

Here we will show you two methods that you can use to simplify the square root of 43632. In other words, we will show you how to find the square root of 43632 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.

√43632 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43632 to simplify the square root of 43632. 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 43632. The factors of 43632 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 101, 108, 144, 202, 216, 303, 404, 432, 606, 808, 909, 1212, 1616, 1818, 2424, 2727, 3636, 4848, 5454, 7272, 10908, 14544, 21816, and 43632. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 43632 divided by the greatest perfect square from the list of all factors of 43632. We determined above that the greatest perfect square from the list of all factors of 43632 is 144. Furthermore, 43632 divided by 144 is 303, therefore B equals 303.

Now we have A and B and can get our answer to 43632 in its simplest radical form as follows:

√43632 = A√B

√43632 = 12√303

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43632 to simplify the square root of 43632 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 43632 and then take the square root of that product. The prime factors that multiply together to make 43632 are 2 x 2 x 2 x 2 x 3 x 3 x 3 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 43632 by the number (A) squared. 12 squared is 144 and 43632 divided by 144 is 303. Therefore, B equals 303.

Once again we have A and B and can get our answer to 43632 in its simplest radical form as follows:

√43632 = A√B

√43632 = 12√303

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