If (2 + 5√3)² = 79 + K√3, then what is the value of K?
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Correct answer: C
Explanation
Given:
(2 + 5√3)² = 79 + K√3
According to the formula:
(a + b)² = a² + b² + 2ab
(2 + 5√3)² = 2² + (5√3)² + 2 × 2 × 5√3
= 4 + 25 × 3 + 20√3
= 4 + 75 + 20√3
= 79 + 20√3
K = 20