Question

Which of these expressions represents the product of an irrational number and a rational number being irrational?

Answer 1

Option B

Step-by-step 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:

`\begin{gathered} 3\cdot\text{ }\sqrt[]{9} \\ \Rightarrow\text{ 3 }\cdot\text{ 3} \\ =\text{ 9 } \end{gathered}`

The correct option is B, because:

`\begin{gathered} (1)/(4)\cdot\text{ }\sqrt[]{44} \\ (1)/(4)\cdot\text{ }\sqrt[]{4\cdot\text{ 11}} \\ (1)/(4)\cdot\text{ 2 }\cdot\text{ }\sqrt[]{11} \\ (1)/(2)\sqrt[]{11} \end{gathered}`

That is an irrational number that is a product of a rational number and an irrational number.

Therefore, the answer is Option B.