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MHTCET 22 Apr 2025 Shift 1 Paper

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Question : 141 of 150

Marks: +1, -0

The approximate value of

\sqrt[3]{64 \cdot 04}

is

4.00043
4.00076
4.00083
4.00064

Solution:

Concept:

Use linear approximation:

f(a+h) \approx f(a) + h f'(a)

.

Explanation:

Let

f(x) = \sqrt[3]{x} = x^{1/3}

.

Then

f'(x) = \frac{1}{3}x^{-2/3} = \frac{1}{3x^{2/3}}

.

Take

a = 64

and

h = 0.04

.

f(64) = \sqrt[3]{64} = 4

.

f'(64) = \frac{1}{3(64)^{2/3}} = \frac{1}{3 \times 16} = \frac{1}{48}

.

Using the approximation:

f(64.04) \approx 4 + 0.04 \times \frac{1}{48}

.

0.04 \times \frac{1}{48} = 0.000833

.

Thus,

\sqrt[3]{64.04} \approx 4.00083

.

Answer:

Option C.

4.00083

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