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PUNE MCA Exam 2014 Question Paper with answers for online practice

Question : 5 of 58

Marks: +1, -0

The cube root of 9√3+11√2 is

Solution:

Concept:

A cube root can be found by assuming a binomial form and expanding.

Explanation:

Let the cube root be

\sqrt{3} + \sqrt{2}

Compute

(\sqrt{3} + \sqrt{2})^3

= (\sqrt{3})^3 + 3(\sqrt{3})^2\sqrt{2} + 3\sqrt{3}(\sqrt{2})^2 + (\sqrt{2})^3

= 3\sqrt{3} + 3 \cdot 3 \cdot \sqrt{2} + 3 \cdot \sqrt{3} \cdot 2 + 2\sqrt{2}

= 3\sqrt{3} + 9\sqrt{2} + 6\sqrt{3} + 2\sqrt{2}

= 9\sqrt{3} + 11\sqrt{2}

Thus cube root is

\sqrt{3} + \sqrt{2}

Answer:

Option D.

\sqrt{3} + \sqrt{2}

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