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 multiplyingradical expressions states that if sqrt(a) and sqrt(b) are real numbers, then csqrt(a)* dsqrt(b) = cdsqrt(a b).
5sqrt(50x^5y^3) * 2sqrt(48xy)=5(2)sqrt(50x^5y^3 * 48xy)
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 and the roots are even, 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, x and y.
In the first radical, the index is even, while the exponent of x is odd and the exponent of y is odd. Therefore, in order for this radical expression to result in a real number, both x and y must be either positive or negative.
In the second radical, the index is even while the exponent of x is odd and the exponent of y is odd. Therefore, in order for this radical expression to result in a real number, both x and y must be either positive or negative.
This means that if we remove x or y from the radical, we will not need absolute value symbols.
