Question

Q.2 The approximate value of 3 root 66 is​

Answer 1

Answer:

it's 24.3721152

Step-by-step explanation:

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Answer 2

We can use differential to find the approximate value of (66)^1/3

Let f(x) = x^1/3

Derivate of f(x) = 1/3x^(2/3)

Suppose, x = 64,Δx = 2.

Then, x + Δx = 64+2 = 66.

We know,

f( x + Δx) - f(x) = f'(x).Δx

f(66) - f(64) = f'(64).(2)

(66)^1/3 - (64)^1/3 = 1/3(64)^(2/3) * 2

(66)^1/3 = 4+ 2/48 = 97/24 ≈ 4.0416

Hence, 66^(1/3) or ∛66 = 4.0416