Simplify Square Root of 75779

Here we will show you two methods that you can use to simplify the square root of 75779. In other words, we will show you how to find the square root of 75779 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.

√75779 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75779 to simplify the square root of 75779. 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 75779. The factors of 75779 are 1, 11, 83, 913, 6889, and 75779. Furthermore, the greatest perfect square on this list is 6889 and the square root of 6889 is 83. Therefore, A equals 83.

B = Calculate 75779 divided by the greatest perfect square from the list of all factors of 75779. We determined above that the greatest perfect square from the list of all factors of 75779 is 6889. Furthermore, 75779 divided by 6889 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 75779 in its simplest radical form as follows:

√75779 = A√B

√75779 = 83√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75779 to simplify the square root of 75779 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 75779 and then take the square root of that product. The prime factors that multiply together to make 75779 are 11 x 83 x 83. When we strip out the pairs only, we get 83 x 83 = 6889 and the square root of 6889 is 83. Therefore, A equals 83.

B = Divide 75779 by the number (A) squared. 83 squared is 6889 and 75779 divided by 6889 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 75779 in its simplest radical form as follows:

√75779 = A√B

√75779 = 83√11

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Simplify Square Root of 75780
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