The approximate value of (0.007)¹/3} is

Correct Answer is : 2312023/12012023

Correct Answer is : 2312023/12012023

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MHTCET 15 Apr 2026 Shift 2 Paper

Question : 105 of 150

Marks: +1, -0

(0.007)^{\frac{1}{3}}

Solution:

Concept:

Cube root of a decimal can be found by writing it as a fraction with a perfect cube denominator.

Explanation:

We need to find

(0.007)^{\frac{1}{3}}

Write

0.007 = \frac{7}{1000}

So,

(0.007)^{\frac{1}{3}} = \left(\frac{7}{1000}\right)^{\frac{1}{3}}

Since

1000 = 10^3

, we have

\sqrt[3]{1000} = 10

Thus,

(0.007)^{\frac{1}{3}} = \frac{\sqrt[3]{7}}{10}

Using

\sqrt[3]{7} \approx 1.913

, we get

\frac{1.913}{10} \approx 0.1913

Now compare this with the given options.

\frac{21}{120} = 0.175

\frac{23}{120} \approx 0.1917

\frac{29}{120} \approx 0.2417

\frac{31}{120} \approx 0.2583

The closest value to

0.1913

0.1917

Answer:

\frac{23}{120}

(Option B)

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