Simplify Square Root of 88872

Here we will show you two methods that you can use to simplify the square root of 88872. In other words, we will show you how to find the square root of 88872 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.

√88872 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88872 to simplify the square root of 88872. 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 88872. The factors of 88872 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 23, 24, 28, 42, 46, 56, 69, 84, 92, 138, 161, 168, 184, 276, 322, 483, 529, 552, 644, 966, 1058, 1288, 1587, 1932, 2116, 3174, 3703, 3864, 4232, 6348, 7406, 11109, 12696, 14812, 22218, 29624, 44436, and 88872. Furthermore, the greatest perfect square on this list is 2116 and the square root of 2116 is 46. Therefore, A equals 46.

B = Calculate 88872 divided by the greatest perfect square from the list of all factors of 88872. We determined above that the greatest perfect square from the list of all factors of 88872 is 2116. Furthermore, 88872 divided by 2116 is 42, therefore B equals 42.

Now we have A and B and can get our answer to 88872 in its simplest radical form as follows:

√88872 = A√B

√88872 = 46√42

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88872 to simplify the square root of 88872 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 88872 and then take the square root of that product. The prime factors that multiply together to make 88872 are 2 x 2 x 2 x 3 x 7 x 23 x 23. When we strip out the pairs only, we get 2 x 2 x 23 x 23 = 2116 and the square root of 2116 is 46. Therefore, A equals 46.

B = Divide 88872 by the number (A) squared. 46 squared is 2116 and 88872 divided by 2116 is 42. Therefore, B equals 42.

Once again we have A and B and can get our answer to 88872 in its simplest radical form as follows:

√88872 = A√B

√88872 = 46√42

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