Simplify Square Root of 81733

Here we will show you two methods that you can use to simplify the square root of 81733. In other words, we will show you how to find the square root of 81733 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.

√81733 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81733 to simplify the square root of 81733. 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 81733. The factors of 81733 are 1, 37, 47, 1739, 2209, and 81733. Furthermore, the greatest perfect square on this list is 2209 and the square root of 2209 is 47. Therefore, A equals 47.

B = Calculate 81733 divided by the greatest perfect square from the list of all factors of 81733. We determined above that the greatest perfect square from the list of all factors of 81733 is 2209. Furthermore, 81733 divided by 2209 is 37, therefore B equals 37.

Now we have A and B and can get our answer to 81733 in its simplest radical form as follows:

√81733 = A√B

√81733 = 47√37

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81733 to simplify the square root of 81733 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 81733 and then take the square root of that product. The prime factors that multiply together to make 81733 are 37 x 47 x 47. When we strip out the pairs only, we get 47 x 47 = 2209 and the square root of 2209 is 47. Therefore, A equals 47.

B = Divide 81733 by the number (A) squared. 47 squared is 2209 and 81733 divided by 2209 is 37. Therefore, B equals 37.

Once again we have A and B and can get our answer to 81733 in its simplest radical form as follows:

√81733 = A√B

√81733 = 47√37

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Simplify Square Root of 81734
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