Simplify Square Root of 40328

Here we will show you two methods that you can use to simplify the square root of 40328. In other words, we will show you how to find the square root of 40328 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.

√40328 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40328 to simplify the square root of 40328. 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 40328. The factors of 40328 are 1, 2, 4, 8, 71, 142, 284, 568, 5041, 10082, 20164, and 40328. Furthermore, the greatest perfect square on this list is 20164 and the square root of 20164 is 142. Therefore, A equals 142.

B = Calculate 40328 divided by the greatest perfect square from the list of all factors of 40328. We determined above that the greatest perfect square from the list of all factors of 40328 is 20164. Furthermore, 40328 divided by 20164 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 40328 in its simplest radical form as follows:

√40328 = A√B

√40328 = 142√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40328 to simplify the square root of 40328 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 40328 and then take the square root of that product. The prime factors that multiply together to make 40328 are 2 x 2 x 2 x 71 x 71. When we strip out the pairs only, we get 2 x 2 x 71 x 71 = 20164 and the square root of 20164 is 142. Therefore, A equals 142.

B = Divide 40328 by the number (A) squared. 142 squared is 20164 and 40328 divided by 20164 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 40328 in its simplest radical form as follows:

√40328 = A√B

√40328 = 142√2

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Simplify Square Root of 40329
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