Simplify Square Root of 75796

Here we will show you two methods that you can use to simplify the square root of 75796. In other words, we will show you how to find the square root of 75796 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.

√75796 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75796 to simplify the square root of 75796. 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 75796. The factors of 75796 are 1, 2, 4, 7, 14, 28, 2707, 5414, 10828, 18949, 37898, and 75796. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 75796 divided by the greatest perfect square from the list of all factors of 75796. We determined above that the greatest perfect square from the list of all factors of 75796 is 4. Furthermore, 75796 divided by 4 is 18949, therefore B equals 18949.

Now we have A and B and can get our answer to 75796 in its simplest radical form as follows:

√75796 = A√B

√75796 = 2√18949

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75796 to simplify the square root of 75796 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 75796 and then take the square root of that product. The prime factors that multiply together to make 75796 are 2 x 2 x 7 x 2707. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 75796 by the number (A) squared. 2 squared is 4 and 75796 divided by 4 is 18949. Therefore, B equals 18949.

Once again we have A and B and can get our answer to 75796 in its simplest radical form as follows:

√75796 = A√B

√75796 = 2√18949

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Simplify Square Root of 75797
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