Question : The positive square root of [0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4 (0.6 + 0.4)] is equal to:
Option 1: 2.1736
Option 2: 1
Option 3: 0.21736
Option 4: 0.072
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Correct Answer: 1
Solution : 0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4 (0.6 + 0.4) = 0.6 3 + 0.4 3 + 3 × 0.6 × 0.4 (0.6 + 0.4) The equation is in the form of (a + b) 3 = a 3 + b 3 + 3ab (a + b) So, 0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4 (0.6 + 0.4) = (0.6 + 0.4) 3 = 1 3 = 1 Hence, the correct answer is 1.
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