Find the value of √(9 + 4√5) + √(9 - 4√5).
Show answer & explanation
Correct answer: B
Explanation
Given:
√(9 + 4√5) + √(9 − 4√5)
By the formula:
√(a + b + 2√ab) = √a + √b
9 + 4√5 = 5 + 4 + 2√(5 × 4)
√(9 + 4√5) = √5 + 2
9 − 4√5 = 5 + 4 − 2√(5 × 4)
√(9 − 4√5) = √5 − 2
(√5 + 2) + (√5 − 2) = 4.47
Nearest value in the given options = 4