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UPTET Paper 1 2022 Solved Paper

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Question : 102 of 150

Marks: +1, -0

The square root of 7 + 2√10 is

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

Solution:

Concept:

Use the perfect square identity:

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

. Rewrite the given number as a perfect square of a binomial.

Explanation:

Write

7 + 2\sqrt{10}

as

2 + 5 + 2\sqrt{2 \times 5}

.

Express it as

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

.

This matches the form

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

.

The square root of

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

is

\sqrt{2} + \sqrt{5}

(positive root).

Answer:

C.

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

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