Simplify Square Root of 10769

Here we will show you two methods that you can use to simplify the square root of 10769. In other words, we will show you how to find the square root of 10769 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.

√10769 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10769 to simplify the square root of 10769. 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 10769. The factors of 10769 are 1, 11, 89, 121, 979, and 10769. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 10769 divided by the greatest perfect square from the list of all factors of 10769. We determined above that the greatest perfect square from the list of all factors of 10769 is 121. Furthermore, 10769 divided by 121 is 89, therefore B equals 89.

Now we have A and B and can get our answer to 10769 in its simplest radical form as follows:

√10769 = A√B

√10769 = 11√89

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10769 to simplify the square root of 10769 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 10769 and then take the square root of that product. The prime factors that multiply together to make 10769 are 11 x 11 x 89. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 10769 by the number (A) squared. 11 squared is 121 and 10769 divided by 121 is 89. Therefore, B equals 89.

Once again we have A and B and can get our answer to 10769 in its simplest radical form as follows:

√10769 = A√B

√10769 = 11√89

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Simplify Square Root of 10770
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