Simplify Square Root of 73728

Here we will show you two methods that you can use to simplify the square root of 73728. In other words, we will show you how to find the square root of 73728 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.

√73728 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73728 to simplify the square root of 73728. 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 73728. The factors of 73728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2048, 2304, 3072, 4096, 4608, 6144, 8192, 9216, 12288, 18432, 24576, 36864, and 73728. Furthermore, the greatest perfect square on this list is 36864 and the square root of 36864 is 192. Therefore, A equals 192.

B = Calculate 73728 divided by the greatest perfect square from the list of all factors of 73728. We determined above that the greatest perfect square from the list of all factors of 73728 is 36864. Furthermore, 73728 divided by 36864 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 73728 in its simplest radical form as follows:

√73728 = A√B

√73728 = 192√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73728 to simplify the square root of 73728 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 73728 and then take the square root of that product. The prime factors that multiply together to make 73728 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 36864 and the square root of 36864 is 192. Therefore, A equals 192.

B = Divide 73728 by the number (A) squared. 192 squared is 36864 and 73728 divided by 36864 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 73728 in its simplest radical form as follows:

√73728 = A√B

√73728 = 192√2

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Simplify Square Root of 73729
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