To simplify the expression, be sure to check the index of each radical.
12|x| ysqrt(42)
Practice makes perfect
Before multiplying the given radical expressions, we need to answer two questions.
Can the expressions be multiplied?
If so, do absolute value symbols need to be added to the answer?
The rule regarding multiplying radical expressions states: If sqrt(a) and sqrt(b) are real numbers, then sqrt(a)*sqrt(b)=sqrt(a b).4sqrt(6y)* 3sqrt(7x^2y)=12sqrt(6y* 7x^2y)
Because we are assuming that both radicals are real numbers and we can see that the given expressions have the same index, we can multiply them. Now, to answer the second question, consider the rule regarding absolute value symbols.
For any real number a:
sqrt(a^n)=
a if n is odd
|a| if n is even
Since both radicals are real numbers, the roots are even, and the expressions underneath the radicals are positive. Otherwise, the radicals would be imaginary. With this in mind, let's consider the possible values of the variables, y and x.
In the first radical, the index is even and the exponent of y is odd. Therefore, in order for this radical expression to result in a real number, y must be positive.
In the second radical, the index is even and the exponent of x is even. Therefore, the expression will be real whether the value of x is positive or negative.
Because our radical has an even root and the variable x has an even exponent and y is positive, we will need to use absolute value symbol to simplify our expression.
