Simplify Square Root of 33777

Here we will show you two methods that you can use to simplify the square root of 33777. In other words, we will show you how to find the square root of 33777 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.

√33777 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 33777 to simplify the square root of 33777. 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 33777. The factors of 33777 are 1, 3, 9, 27, 81, 139, 243, 417, 1251, 3753, 11259, and 33777. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 33777 divided by the greatest perfect square from the list of all factors of 33777. We determined above that the greatest perfect square from the list of all factors of 33777 is 81. Furthermore, 33777 divided by 81 is 417, therefore B equals 417.

Now we have A and B and can get our answer to 33777 in its simplest radical form as follows:

√33777 = A√B

√33777 = 9√417

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 33777 to simplify the square root of 33777 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 33777 and then take the square root of that product. The prime factors that multiply together to make 33777 are 3 x 3 x 3 x 3 x 3 x 139. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 33777 by the number (A) squared. 9 squared is 81 and 33777 divided by 81 is 417. Therefore, B equals 417.

Once again we have A and B and can get our answer to 33777 in its simplest radical form as follows:

√33777 = A√B

√33777 = 9√417

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Simplify Square Root of 33778
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