Given √24 ≈ 4.899, compute the exact value of √(8/3) using this information.

Introduction / Context:We are to evaluate √(8/3) using the given approximation for √24, observing the algebraic relation between the two expressions. Recognizing equivalent forms simplifies computation.

Given Data / Assumptions:√24 ≈ 4.899. We need √(8/3).

Concept / Approach:Note that 8/3 = 24/9. Therefore √(8/3) = √(24/9) = √24 / √9 = √24 / 3. Use the provided √24 value and divide by 3.

Step-by-Step Solution:

Verification / Alternative check:Square 1.633: approximately 2.666, close to 8/3 ≈ 2.666..., confirming consistency.

Why Other Options Are Wrong:0.544 and 1.333 are too small; 2.666 is the square (not the root); 1.414 is √2, not √(8/3).

Common Pitfalls:Confusing √(a/b) with a/b of square roots or squaring mistakenly; always use √(a/b) = √a / √b.

Final Answer:1.633