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UPTET Paper 1 2017 Solved Paper

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Question : 92 of 150

Marks: +1, -0

The square root of 7 + 2√10 is

$(√6 + 1)$
$(√3 + 2)$
(√2 + √5)
$(2 + √5)$

Solution:

Concept:

The expression

7 + 2\sqrt{10}

can be written as a perfect square of a binomial

(a+b)^2

.

Explanation:

Rewrite

7

as

(\sqrt{2})^2 + (\sqrt{5})^2

.

Note that

2\sqrt{10} = 2 \cdot \sqrt{2} \cdot \sqrt{5}

.

Thus,

7 + 2\sqrt{10} = (\sqrt{2})^2 + (\sqrt{5})^2 + 2\cdot\sqrt{2}\cdot\sqrt{5} = (\sqrt{2} + \sqrt{5})^2

.

Taking the square root gives

\sqrt{(\sqrt{2} + \sqrt{5})^2} = \sqrt{2} + \sqrt{5}

.

Answer:

Option C:

(\sqrt{2} + \sqrt{5})

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