Use the given square-root value to evaluate a related root: If √15 = 3.88, compute the numerical value of √(5/3). Show the relationship that links these two quantities and give the result to two decimal places.

Introduction / Context:This question tests proportional reasoning with square roots. When a square root of a product is known (here √15), you can form related roots such as √(5/3) by using basic root properties. The goal is to connect √(5/3) to √15 cleanly and compute a decimal answer without a calculator-heavy approach.

Given Data / Assumptions:

• Given: √15 = 3.88 (use this value as exact for the problem).
• Find: √(5/3).
• Standard property: √(a/b) = √a / √b for a, b > 0.

Concept / Approach:Rewrite 5/3 as 15/9 so that its square root links directly to √15. Since √(15/9) = √15 / √9 and √9 = 3, we obtain a simple division of the provided value 3.88 by 3. This avoids approximations beyond the given data and keeps the computation short and reliable.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 0.43: Much too small; would imply √(5/3) < 1.
• 1.63 and 1.89: Too large; they would correspond to squaring above the target 1.6667 baseline.

Common Pitfalls:

• Forgetting to take √9 = 3 when converting 5/3 to 15/9.
• Rounding too early; compute 3.88 / 3 first, then round.

Final Answer: