Notice that when a and b are both negative the expression underneath the radical is positive. What are the possible values for a and b? Remember that the square root of a negative number raised to the power of 2 is equal to the absolute value of that number.
2|b|sqrt(5ab)
Practice makes perfect
Consider the given radical expression.
sqrt(20ab^3)
The expression underneath the radical is non-negative. Otherwise, the radical would be imaginary. With this in mind, let's consider the possible values of the variables, a and b.
The product of a and b^3 must be non-negative — a and b^3 must have the same sign or one of them can be 0 and the other can be either positive or negative.
If a and b^3 have the same sign, then a and b^3 can both be either positive, negative, or zero.
Because a and b can be negative, when we remove either of them from the radical we will need absolute value symbols.
