Simplify Square Root of 84960

Here we will show you two methods that you can use to simplify the square root of 84960. In other words, we will show you how to find the square root of 84960 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.

√84960 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84960 to simplify the square root of 84960. 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 84960. The factors of 84960 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 59, 60, 72, 80, 90, 96, 118, 120, 144, 160, 177, 180, 236, 240, 288, 295, 354, 360, 472, 480, 531, 590, 708, 720, 885, 944, 1062, 1180, 1416, 1440, 1770, 1888, 2124, 2360, 2655, 2832, 3540, 4248, 4720, 5310, 5664, 7080, 8496, 9440, 10620, 14160, 16992, 21240, 28320, 42480, and 84960. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 84960 divided by the greatest perfect square from the list of all factors of 84960. We determined above that the greatest perfect square from the list of all factors of 84960 is 144. Furthermore, 84960 divided by 144 is 590, therefore B equals 590.

Now we have A and B and can get our answer to 84960 in its simplest radical form as follows:

√84960 = A√B

√84960 = 12√590

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84960 to simplify the square root of 84960 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 84960 and then take the square root of that product. The prime factors that multiply together to make 84960 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 59. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 84960 by the number (A) squared. 12 squared is 144 and 84960 divided by 144 is 590. Therefore, B equals 590.

Once again we have A and B and can get our answer to 84960 in its simplest radical form as follows:

√84960 = A√B

√84960 = 12√590

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