Simplify Square Root of 72128

Here we will show you two methods that you can use to simplify the square root of 72128. In other words, we will show you how to find the square root of 72128 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.

√72128 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72128 to simplify the square root of 72128. 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 72128. The factors of 72128 are 1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 49, 56, 64, 92, 98, 112, 161, 184, 196, 224, 322, 368, 392, 448, 644, 736, 784, 1127, 1288, 1472, 1568, 2254, 2576, 3136, 4508, 5152, 9016, 10304, 18032, 36064, and 72128. Furthermore, the greatest perfect square on this list is 3136 and the square root of 3136 is 56. Therefore, A equals 56.

B = Calculate 72128 divided by the greatest perfect square from the list of all factors of 72128. We determined above that the greatest perfect square from the list of all factors of 72128 is 3136. Furthermore, 72128 divided by 3136 is 23, therefore B equals 23.

Now we have A and B and can get our answer to 72128 in its simplest radical form as follows:

√72128 = A√B

√72128 = 56√23

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72128 to simplify the square root of 72128 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 72128 and then take the square root of that product. The prime factors that multiply together to make 72128 are 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 23. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 = 3136 and the square root of 3136 is 56. Therefore, A equals 56.

B = Divide 72128 by the number (A) squared. 56 squared is 3136 and 72128 divided by 3136 is 23. Therefore, B equals 23.

Once again we have A and B and can get our answer to 72128 in its simplest radical form as follows:

√72128 = A√B

√72128 = 56√23

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