Simplify Square Root of 77120

Here we will show you two methods that you can use to simplify the square root of 77120. In other words, we will show you how to find the square root of 77120 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.

√77120 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77120 to simplify the square root of 77120. 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 77120. The factors of 77120 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 241, 320, 482, 964, 1205, 1928, 2410, 3856, 4820, 7712, 9640, 15424, 19280, 38560, and 77120. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 77120 divided by the greatest perfect square from the list of all factors of 77120. We determined above that the greatest perfect square from the list of all factors of 77120 is 64. Furthermore, 77120 divided by 64 is 1205, therefore B equals 1205.

Now we have A and B and can get our answer to 77120 in its simplest radical form as follows:

√77120 = A√B

√77120 = 8√1205

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77120 to simplify the square root of 77120 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 77120 and then take the square root of that product. The prime factors that multiply together to make 77120 are 2 x 2 x 2 x 2 x 2 x 2 x 5 x 241. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 77120 by the number (A) squared. 8 squared is 64 and 77120 divided by 64 is 1205. Therefore, B equals 1205.

Once again we have A and B and can get our answer to 77120 in its simplest radical form as follows:

√77120 = A√B

√77120 = 8√1205

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