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MHTCET 11 Apr 2026 Shift 1 Paper

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Question : 126 of 150

Marks: +1, -0

The approximate value of

\sqrt[3]{63}

is

3.9791
3.8791
3.9581
4.0205

Solution:

Concept:

Use the linear approximation formula for a small change near a known perfect cube.

Explanation:

Let

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

and choose

a = 64

, since

\sqrt[3]{64} = 4

.

The approximation formula is

f(a + \Delta x) \approx f(a) + f'(a)\Delta x

.

Here,

63 = 64 + (-1)

, so

\Delta x = -1

.

Now,

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

.

At

x = 64

, we get

f'(64) = \frac{1}{3(64)^{2/3}} = \frac{1}{3 \times 4^2} = \frac{1}{48}

.

Therefore,

\sqrt[3]{63} \approx 4 + \left(\frac{1}{48}\right)(-1)

.

This gives

4 - \frac{1}{48} = 4 - 0.020833 = 3.979167

.

Rounded to four decimal places,

\sqrt[3]{63} \approx 3.9791

.

Answer:

Option A:

3.9791

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