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UPSC CDS 2 2019 Math Paper

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Question : 76 of 100

Marks: +1, -0

What is the square root of 16 + 6√7?

$4 + \sqrt{7}$
4 – √7
$3 + \sqrt{7}$
3 – √7

Solution:

Concept:

Simplify the expression

(a+b)^2 = a^2 + 2ab + b^2

form.

Explanation:

We need to rewrite

16 + 6\sqrt{7}

as a perfect square.

Write

16

as

9 + 7

.

So,

16 + 6\sqrt{7} = 9 + 7 + 6\sqrt{7}

.

Now,

9 = 3^2

and

7 = (\sqrt{7})^2

.

Thus,

3^2 + (\sqrt{7})^2 + 2 \times 3 \times \sqrt{7} = (3 + \sqrt{7})^2

.

Therefore, the square root of

16 + 6\sqrt{7}

is

3 + \sqrt{7}

.

Answer:

C.

3 + \sqrt{7}

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