Simplify a radical expression by factoring: Evaluate (√24 + √216) / √96.

Introduction / Context:This expression simplifies elegantly by factoring out common square-free parts from each square root. Recognizing multiples of 6 under the radicals is the key.

Given Data / Assumptions:

• Expression: (√24 + √216) / √96.
• All radicals are positive principal roots.

Concept / Approach:Rewrite each radicand as a product of a perfect square and a square-free part, then cancel common factors between numerator and denominator.

Step-by-Step Solution:

Verification / Alternative check:Numeric check: √24 ≈ 4.899, √216 ≈ 14.697, sum ≈ 19.596; √96 ≈ 9.798; ratio ≈ 2.00.

Why Other Options Are Wrong:

• 2√6, 6√2, 2/√6, √6 do not equal the simplified value of the ratio.

Common Pitfalls:Forgetting to factor out the perfect squares or failing to cancel √6 correctly.

Final Answer:2