select the correct answer.

which expression has a value closest to 1? (use 3.14 as the value of $\pi$.)

$\bigcirc$ $\frac{7\pi}{\sqrt{10}}$

$\bigcirc$ $\sqrt{75} - \sqrt{74}$

$\bigcirc$ $\sqrt{37} - \sqrt{26}$

$\bigcirc$ $\frac{3\sqrt{5} - \sqrt{20}}{\sqrt{2}}$

Question

select the correct answer.

which expression has a value closest to 1? (use 3.14 as the value of $\pi$.)

$\bigcirc$ $\frac{7\pi}{\sqrt{10}}$

$\bigcirc$ $\sqrt{75} - \sqrt{74}$

$\bigcirc$ $\sqrt{37} - \sqrt{26}$

$\bigcirc$ $\frac{3\sqrt{5} - \sqrt{20}}{\sqrt{2}}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Square Root Approximation", "Decimal Rounding", "Simplifying Radicals" ], "new_concepts": [], "current_concepts": [ "Square Root Approximation", "Decimal Rounding", "Simplifying Radicals" ] } ## Evaluate each expression numerically $$ \begin{aligned} &\text{Option 1: } \frac{7\pi}{\sqrt{10}} \approx \frac{7 \times 3.14}{3.162} \approx \frac{21.98}{3.162} \approx 6.95\ &\text{Option 2: } \sqrt{75} - \sqrt{74} \approx 8.660 - 8.602 = 0.058\ &\text{Option 3: } \sqrt{37} - \sqrt{26} \approx 6.083 - 5.099 = 0.984\ &\text{Option 4: } \frac{3\sqrt{5} - \sqrt{20}}{\sqrt{2}} = \frac{3\sqrt{5} - 2\sqrt{5}}{\sqrt{2}} = \frac{\sqrt{5}}{\sqrt{2}} = \sqrt{2.5} \approx 1.581 \end{aligned} $$ ## Compare differences to 1 $$ \begin{aligned} &|6.95 - 1| = 5.95\ &|0.058 - 1| = 0.942\ &|0.984 - 1| = 0.016\ &|1.581 - 1| = 0.581 \end{aligned} $$ ## Identify the closest value $$ 0.016 < 0.581 < 0.942 < 5.95 $$

(A) $\frac{7\pi}{\sqrt{10}}$

(B) $\sqrt{75} - \sqrt{74}$

(C) $\sqrt{37} - \sqrt{26}$

(D) $\frac{3\sqrt{5} - \sqrt{20}}{\sqrt{2}}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Square Root Approximation" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate each expression numerically

Compare differences to 1

Identify the closest value

Answer: