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RRB NTPC Mains or Stage 2 Model Paper 6 with solutions

Question : 2 of 119

Marks: +1, -0

What is the square root of 9 + 2 14 ?

Solution:

Concept:

For an expression like

\sqrt{a + 2\sqrt{b}}

, try to express it as a perfect square.

Explanation:

Let

9 + 2\sqrt{14} = (\sqrt{7} + \sqrt{2})^2

Check:

(\sqrt{7})^2 + (\sqrt{2})^2 + 2\sqrt{7}\sqrt{2} = 7 + 2 + 2\sqrt{14}

So,

9 + 2\sqrt{14} = 9 + 2\sqrt{14}

Therefore,

\sqrt{9 + 2\sqrt{14}} = \sqrt{(\sqrt{7} + \sqrt{2})^2}

Taking the positive square root gives

\sqrt{7} + \sqrt{2}

Answer:

\sqrt{7} + \sqrt{2}

, which is option C.

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