Simplify Square Root of 880

Here we will show you two methods that you can use to simplify the square root of 880. In other words, we will show you how to find the square root of 880 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.

√880 = A√B

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

B = Calculate 880 divided by the greatest perfect square from the list of all factors of 880. We determined above that the greatest perfect square from the list of all factors of 880 is 16. Furthermore, 880 divided by 16 is 55, therefore B equals 55.

Now we have A and B and can get our answer to 880 in its simplest radical form as follows:

√880 = A√B

√880 = 4√55

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 880 to simplify the square root of 880 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 880 and then take the square root of that product. The prime factors that multiply together to make 880 are 2 x 2 x 2 x 2 x 5 x 11. 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 880 by the number (A) squared. 4 squared is 16 and 880 divided by 16 is 55. Therefore, B equals 55.

Once again we have A and B and can get our answer to 880 in its simplest radical form as follows:

√880 = A√B

√880 = 4√55

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Simplify Square Root of 881
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