Simplify Square Root of 33976

Here we will show you two methods that you can use to simplify the square root of 33976. In other words, we will show you how to find the square root of 33976 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.

√33976 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 33976 to simplify the square root of 33976. 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 33976. The factors of 33976 are 1, 2, 4, 8, 31, 62, 124, 137, 248, 274, 548, 1096, 4247, 8494, 16988, and 33976. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 33976 divided by the greatest perfect square from the list of all factors of 33976. We determined above that the greatest perfect square from the list of all factors of 33976 is 4. Furthermore, 33976 divided by 4 is 8494, therefore B equals 8494.

Now we have A and B and can get our answer to 33976 in its simplest radical form as follows:

√33976 = A√B

√33976 = 2√8494

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 33976 to simplify the square root of 33976 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 33976 and then take the square root of that product. The prime factors that multiply together to make 33976 are 2 x 2 x 2 x 31 x 137. 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 33976 by the number (A) squared. 2 squared is 4 and 33976 divided by 4 is 8494. Therefore, B equals 8494.

Once again we have A and B and can get our answer to 33976 in its simplest radical form as follows:

√33976 = A√B

√33976 = 2√8494

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Simplify Square Root of 33977
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