For any real number a contained in a radical such that sqrt(a^n), the root is a if n is odd and |a| if n is even.
3|x|y^2 sqrt(6xy)
Practice makes perfect
To simplify radicals, we should recall the rules regarding when the root should be contained inside an absolute value. Consider the following two cases for any real number a.
sqrt(a^n)=
a if n is odd
|a| if n is even
In this case, the index number of the expression is even and the exponents of x and y are odd. For the expression to result in a real number, the product of x and y must be positive. Therefore, x and y must have the same sign — both positive or both negative.
This means that we will need absolute value symbols.
