Simplify Square Root of 40792

Here we will show you two methods that you can use to simplify the square root of 40792. In other words, we will show you how to find the square root of 40792 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.

√40792 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40792 to simplify the square root of 40792. 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 40792. The factors of 40792 are 1, 2, 4, 8, 5099, 10198, 20396, and 40792. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 40792 divided by the greatest perfect square from the list of all factors of 40792. We determined above that the greatest perfect square from the list of all factors of 40792 is 4. Furthermore, 40792 divided by 4 is 10198, therefore B equals 10198.

Now we have A and B and can get our answer to 40792 in its simplest radical form as follows:

√40792 = A√B

√40792 = 2√10198

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40792 to simplify the square root of 40792 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 40792 and then take the square root of that product. The prime factors that multiply together to make 40792 are 2 x 2 x 2 x 5099. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 40792 by the number (A) squared. 2 squared is 4 and 40792 divided by 4 is 10198. Therefore, B equals 10198.

Once again we have A and B and can get our answer to 40792 in its simplest radical form as follows:

√40792 = A√B

√40792 = 2√10198

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Simplify Square Root of 40793
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