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The Difference in Root & Mean Squared

If you are student trying to study the difference between a mean that has been squared and a root that has been squared, you first must learn the definitions of each of these math terms and memorize the procedure for arriving at the answer for each. Practice simple math equations involving both math principles to improve your math muscle.
  1. What is the Mean?

    • The mean is used to describe a set of numbers's central tendency, and is commonly referred to as an average. To find the mean of a set of numbers, you will add the numbers together and divide by the quantity of numbers in the set. Here is an example:

      10 + 5 + 5 + 15 + 20 = 55

      Count the quantity of numbers in the set. In this example, there are 5 numbers in the set. Therefore, 55 / 5 = 11.

      The mean is 11.

    How Do I Calculate Mean Squared?

    • When you square a number you multiply it by itself. A squared number is indicated by the exponent "2" after the number being squared. An example is the following: Square the number 10. This translates to 10 ^ 2 or 10 x 10, which equals 100.

    What is a Square Root?

    • A square root has a different definition and procedure then squaring a number. You will recognize a square root by a radical symbol over and around the number that looks like a check mark. The square root essentially is the opposite of the square. You simplify the square root to get a number that indicates the number you must multiply by itself to indicate the square root. Here is an example:

      1) The square root of 9 is 3 because 3 x 3 = 9.

    How Do I Square a Square Root?

    • Apply your squaring skills to a square root. Place the square root in parantheses and place the exponent "2" outside of the parantheses. This indicates that you should simplify the square root first, then square the number. Here is an example:

      (The square root of 9) raised to the second power.

      Figure out the square root of 9 first. The answer is 3. Then square 3, which is 3 raised to the second power or 3 x 3. You arrive at 9.

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