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.
a^2|b^3|
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 evenSince the radical is a real number and the root is even, the expression underneath the radical is positive. Otherwise, the radical would be imaginary. With this in mind, let's consider the possible values of the variables, a and b.
In the radical, the index is even and the exponent of a is even. Therefore, the expression will be real whether the value of a is positive, negative or equal to 0.
When we find an even root of an even power and the result is an odd power, we must use absolute value of the result. For this reason, we should use an absolute value for b^3
We can now simplify the given radical by writing the expression inside as powers equal to the index number of the radical.
