Simplify Square Root of 10933

Here we will show you two methods that you can use to simplify the square root of 10933. In other words, we will show you how to find the square root of 10933 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.

√10933 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10933 to simplify the square root of 10933. 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 10933. The factors of 10933 are 1, 13, 29, 377, 841, and 10933. Furthermore, the greatest perfect square on this list is 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Calculate 10933 divided by the greatest perfect square from the list of all factors of 10933. We determined above that the greatest perfect square from the list of all factors of 10933 is 841. Furthermore, 10933 divided by 841 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 10933 in its simplest radical form as follows:

√10933 = A√B

√10933 = 29√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10933 to simplify the square root of 10933 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 10933 and then take the square root of that product. The prime factors that multiply together to make 10933 are 13 x 29 x 29. When we strip out the pairs only, we get 29 x 29 = 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Divide 10933 by the number (A) squared. 29 squared is 841 and 10933 divided by 841 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 10933 in its simplest radical form as follows:

√10933 = A√B

√10933 = 29√13

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Simplify Square Root of 10934
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