Evaluate the product of roots: What is √10 × √15 equal to?

Introduction / Context:Products of square roots are simplified using √a * √b = √(ab). Factor the product to extract perfect squares.

Given Data / Assumptions:Compute √10 * √15.

Concept / Approach:Multiply under a single radical: √(10 * 15) = √150. Factor 150 as 25 * 6 to extract a perfect square.

Step-by-Step Solution:

Verification / Alternative check:Approximate: √10 ≈ 3.1623, √15 ≈ 3.8730, product ≈ 12.247; 5√6 ≈ 5 * 2.449 = 12.247. Matches.

Why Other Options Are Wrong:6√5 equals √180, not √150; √30 is too small; 5 is a drastic underestimate; 10√15 is unrelated.

Common Pitfalls:Adding under the radical (√10 + √15) instead of multiplying; not extracting the largest perfect square factor.

Final Answer:5√6