Simplify the expression (√32 + √48) / (√8 + √12), and provide the exact simplified value.

Introduction / Context:
This problem tests simplification of expressions with square roots using factorization of perfect squares and cancellation. The goal is an exact simplified value without decimals.

Given Data / Assumptions:

• Expression: (√32 + √48) / (√8 + √12).
• All terms are positive real numbers.

Concept / Approach:
Express each radicand as a product including a perfect square to simplify: √32 = √(16*2) = 4√2, √48 = √(16*3) = 4√3, √8 = √(4*2) = 2√2, √12 = √(4*3) = 2√3. Then factor and cancel common terms.

Step-by-Step Solution:
√32 = 4√2 and √48 = 4√3. √8 = 2√2 and √12 = 2√3. Numerator: 4√2 + 4√3 = 4(√2 + √3). Denominator: 2√2 + 2√3 = 2(√2 + √3). Ratio = [4(√2 + √3)] / [2(√2 + √3)] = 4 / 2 = 2.

Verification / Alternative check:
Substitute √2 ≈ 1.414 and √3 ≈ 1.732 to compute both numerator and denominator and confirm the quotient is 2.0.

Why Other Options Are Wrong:
√2, 4, and 8 do not follow from the exact cancellations; only 2 results after factoring common (√2 + √3).

Common Pitfalls:
Forgetting to factor out common radicals or attempting to rationalize unnecessarily can complicate the problem. Always reduce radicals first.

Final Answer:
2