Simplify Square Root of 9680

Here we will show you two methods that you can use to simplify the square root of 9680. In other words, we will show you how to find the square root of 9680 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.

√9680 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9680 to simplify the square root of 9680. 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 9680. The factors of 9680 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 121, 176, 220, 242, 440, 484, 605, 880, 968, 1210, 1936, 2420, 4840, and 9680. Furthermore, the greatest perfect square on this list is 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Calculate 9680 divided by the greatest perfect square from the list of all factors of 9680. We determined above that the greatest perfect square from the list of all factors of 9680 is 1936. Furthermore, 9680 divided by 1936 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 9680 in its simplest radical form as follows:

√9680 = A√B

√9680 = 44√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9680 to simplify the square root of 9680 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 9680 and then take the square root of that product. The prime factors that multiply together to make 9680 are 2 x 2 x 2 x 2 x 5 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 11 x 11 = 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Divide 9680 by the number (A) squared. 44 squared is 1936 and 9680 divided by 1936 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 9680 in its simplest radical form as follows:

√9680 = A√B

√9680 = 44√5

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Simplify Square Root of 9681
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