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1. Taking the square root helps normalize a distribution skewed right.
When one applies a square root transformation, the square root of every value is taken. However, as one cannot take the square root of a negative number, if there are negative values for a variable, a constant must be added to move the minimum value of the distribution above 0, preferably to 1.00 (the rationale for this assertion is explained below). Another important point is that numbers of 1.00 and above behave differently than numbers between 0.00 and 0.99. The square root of numbers above 1.00 always become smaller, 1.00 and 0.00 remain constant, and number between 0.00 and 1.00 become larger (the square root of 4 is 2, but the square root of 0.40 is 0.63). Thus, if you apply a square root to a continuous variable that contains values between 0 and 1 as well as above 1, you are treating some numbers differently than others, which is probably not desirable in most cases.
2. Taking the logarithm of X also helps normalize a right-skewed distribution.
Logarithmic transformations are actually a class of transformations, rather than a single transformation. In brief, a logarithm is the power (exponent) to which a base number must be raised in order to get the original number. Any given number can be expressed as y to the x power in an infinite number of ways. For example, if we were talking about base 10, 1 is 100, 100 is 102, 16 is 101.2, and so on. Thus, log10(100)=2 and log10(16)=1.2. However, base 10 is not the only option for log transformations. Another common option is the Natural Logarithm, where the constant e (2.7182818) is the base. In this case the natural log 100 is 4.605. As the logarithm of any negative number or number less than 1 is undefined, if a variable contains values less than 1.0, a constant must be added to move the minimum value of the distribution, preferably to 1.00.
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