Simplify Square Root of 2888

Here we will show you two methods that you can use to simplify the square root of 2888. In other words, we will show you how to find the square root of 2888 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.

√2888 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2888 to simplify the square root of 2888. 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 2888. The factors of 2888 are 1, 2, 4, 8, 19, 38, 76, 152, 361, 722, 1444, and 2888. Furthermore, the greatest perfect square on this list is 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Calculate 2888 divided by the greatest perfect square from the list of all factors of 2888. We determined above that the greatest perfect square from the list of all factors of 2888 is 1444. Furthermore, 2888 divided by 1444 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 2888 in its simplest radical form as follows:

√2888 = A√B

√2888 = 38√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2888 to simplify the square root of 2888 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 2888 and then take the square root of that product. The prime factors that multiply together to make 2888 are 2 x 2 x 2 x 19 x 19. When we strip out the pairs only, we get 2 x 2 x 19 x 19 = 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Divide 2888 by the number (A) squared. 38 squared is 1444 and 2888 divided by 1444 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 2888 in its simplest radical form as follows:

√2888 = A√B

√2888 = 38√2

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Simplify Square Root of 2889
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