Solution: ∛129
Given: ∛129 = ?
We know that:
5³ = 125
6³ = 216
Since 129 is very close to 125, let
∛129 = 5 + x
Using the approximation formula:
(a + x)³ ≈ a³ + 3a²x
129 ≈ 125 + 3(5²)x
129 ≈ 125 + 75x
4 = 75x
x = 4/75
x ≈ 0.0533
∛129 ≈ 5 + 0.0533
∛129 ≈ 5.053
Answer: ∛129 ≈ 5.053
