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For any positive real numbers a and b, the identity √a × √b = √(ab) holds. What if BOTH a and b are NEGATIVE?
AThe identity FAILS — √(-1)√(-1) = i² = -1, NOT √((-1)(-1)) = 1
BThe identity still holds — √(-1)√(-1) = √1 = 1
CThe identity holds only if a = b
DBoth sides equal i
Answer & Solution
Correct answer: A. The identity FAILS — √(-1)√(-1) = i² = -1, NOT √((-1)(-1)) = 1
The identity √a × √b = √(ab) does NOT hold when both a and b are negative. If it did, √(-1) × √(-1) = √1 = 1, contradicting i² = -1. So the rule holds only when at least one of a, b is non-negative.
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