<p>The GM between <em>√9</em> and <em>√16</em>, is</p>
Step-by-Step Solution
Key Concept: The Geometric Mean (GM) of two positive numbers a and b is defined as √(ab). We need to find the GM of √9 and √16 by multiplying them under a single square root.
<p><strong>Step 1:</strong> Identify the two numbers: a = √9 and b = √16</p><p><strong>Step 2:</strong> Recall the formula for Geometric Mean of two numbers: GM = √(ab)</p><p><strong>Step 3:</strong> Apply the formula: GM = √(√9 × √16)</p><p><strong>Step 4:</strong> Simplify the product under the square root: √9 × √16 = √(9 × 16) = √144</p><p><strong>Step 5:</strong> Therefore, GM = √(√144) = √(√(144)) = √(12²) = √12</p><p><strong>Alternative approach:</strong> GM = √(√9 × √16) = (9)^(1/4) × (16)^(1/4) = (9 × 16)^(1/4) = (144)^(1/4) = (12²)^(1/4) = 12^(1/2) = √12</p><p><strong>Verification:</strong> √12 = √(4 × 3) = 2√3 ≈ 3.464, which lies between √9 = 3 and √16 = 4, as expected for the GM.</p><p><strong>∴ Answer:</strong> b</p>
Correct Answer: b