which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?

$\sqrt{11} \times \sqrt{11}$

$4.7813265... \times \sqrt{5}$

$\pi \times 3.785492...$

$\sqrt{21} \times \pi$

Question

which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?

$\sqrt{11} \times \sqrt{11}$

$4.7813265... \times \sqrt{5}$

$\pi \times 3.785492...$

$\sqrt{21} \times \pi$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Irrational Numbers" ], "new_concepts": [], "current_concepts": [ "Irrational Numbers", "Number Classification" ] } ## Identify the irrational factors in each expression $$ \begin{aligned} &\text{Option 1: } \sqrt{11} \text{ and } \sqrt{11} \text{ are both irrational.}\ &\text{Option 2: } 4.7813265\dots \text{ and } \sqrt{5} \text{ are both irrational.}\ &\text{Option 3: } \pi \text{ and } 3.785492\dots \text{ are both irrational.}\ &\text{Option 4: } \sqrt{21} \text{ and } \pi \text{ are both irrational.} \end{aligned} $$ ## Evaluate the product of each expression $$ \begin{aligned} &\sqrt{11} \times \sqrt{11} = 11 \quad (\text{Rational})\ &4.7813265\dots \times \sqrt{5} \quad (\text{Irrational})\ &\pi \times 3.785492\dots \quad (\text{Irrational})\ &\sqrt{21} \times \pi \quad (\text{Irrational}) \end{aligned} $$ ## Select the expression with a rational product $$ \sqrt{11} \times \sqrt{11} = 11 $$

(A) $\sqrt{11} \times \sqrt{11}$

(B) $4.7813265\dots \times \sqrt{5}$

(C) $\pi \times 3.785492\dots$

(D) $\sqrt{21} \times \pi$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Number Theory", "Irrational Numbers" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the irrational factors in each expression

Evaluate the product of each expression

Select the expression with a rational product

Answer: