Simplify Square Root of 77936

Here we will show you two methods that you can use to simplify the square root of 77936. In other words, we will show you how to find the square root of 77936 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.

√77936 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77936 to simplify the square root of 77936. 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 77936. The factors of 77936 are 1, 2, 4, 8, 16, 4871, 9742, 19484, 38968, and 77936. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 77936 divided by the greatest perfect square from the list of all factors of 77936. We determined above that the greatest perfect square from the list of all factors of 77936 is 16. Furthermore, 77936 divided by 16 is 4871, therefore B equals 4871.

Now we have A and B and can get our answer to 77936 in its simplest radical form as follows:

√77936 = A√B

√77936 = 4√4871

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77936 to simplify the square root of 77936 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 77936 and then take the square root of that product. The prime factors that multiply together to make 77936 are 2 x 2 x 2 x 2 x 4871. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 77936 by the number (A) squared. 4 squared is 16 and 77936 divided by 16 is 4871. Therefore, B equals 4871.

Once again we have A and B and can get our answer to 77936 in its simplest radical form as follows:

√77936 = A√B

√77936 = 4√4871

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Simplify Square Root of 77937
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