Evaluate √[(7 + 3√5)(7 − 3√5)].

Problem restatementCompute the principal square root of the product (7 + 3√5)(7 − 3√5).

Concept/ApproachUse the identity (a + b)(a − b) = a² − b².

Step-by-step calculation (7 + 3√5)(7 − 3√5) = 7² − (3√5)² = 49 − 9×5 = 49 − 45 = 4 √4 (principal) = 2

Common pitfalls

• Reporting ±2; by convention, “square root” means the non-negative principal root.

Final Answer2