Simplify the ratio of square roots: What is √288 / √128 equal to (in simplest form)?

Introduction / Context:
Ratios of square roots can be simplified by combining under one radical and reducing the fraction before taking the square root.

Given Data / Assumptions:
Expression: √288 / √128.

Concept / Approach:
Use √a / √b = √(a/b). Reduce 288/128 to lowest terms first, then take the square root to avoid messy radicals.

Step-by-Step Solution:

Verification / Alternative check:
Factor approach: 288 = 2^5 * 3^2; 128 = 2^7. Then √288 = 2^2 * 3 * √2 = 12√2; √128 = 2^3 * √2 = 8√2; ratio = (12√2)/(8√2) = 3/2.

Why Other Options Are Wrong:
√3/2 and √6/2 retain radicals unnecessarily; 3/√2 is not equal to 3/2 here; 2/3 is the reciprocal.

Common Pitfalls:
Not simplifying the fraction under the radical or canceling √2 incorrectly.

Final Answer:
3/2