ANSWER
Option B
EXPLANATION
We want to find which of the expressions is in the form:
Irrational number * Rational number = Irrational Number
An irrational number is a number that cannot be expressed as a ratio or fraction of two integers, such as pi or roots.
Options A and C cannot be correct because they each have two irrational numbers multiplying one another.
Simplifying Option D, we have:
[tex]\begin{gathered} 3\cdot\text{ }\sqrt[]{9} \\ \Rightarrow\text{ 3 }\cdot\text{ 3} \\ =\text{ 9 } \end{gathered}[/tex]
The correct option is B, because:
[tex]\begin{gathered} \frac{1}{4}\cdot\text{ }\sqrt[]{44} \\ \frac{1}{4}\cdot\text{ }\sqrt[]{4\cdot\text{ 11}} \\ \frac{1}{4}\cdot\text{ 2 }\cdot\text{ }\sqrt[]{11} \\ \frac{1}{2}\sqrt[]{11} \end{gathered}[/tex]
That is an irrational number that is a product of a rational number and an irrational number.
Therefore, the answer is Option B.
