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UPTET Paper 2 Math and Science Model Test 5

Section: Mathematics and Science

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Question : 131 of 150

Marks: +1, -0

Value of

\sqrt{-\sqrt{3}+\sqrt{84+18\sqrt{3}}}

is

√3
3
-√3
0

Solution:

Concept:

Recognise the inner expression as a perfect square of the form

(a+b)^2

.

Formula:

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

Solution:

Start with

\sqrt{-\sqrt{3}+\sqrt{84+18\sqrt{3}}}

.

Rewrite

84+18\sqrt{3}

as

81 + 3 + 2\cdot 9 \cdot \sqrt{3}

.

This equals

(9+\sqrt{3})^2

because

9^2=81

,

(\sqrt{3})^2=3

, and

2\cdot 9 \cdot \sqrt{3}=18\sqrt{3}

.

So

\sqrt{84+18\sqrt{3}} = 9+\sqrt{3}

(positive square root).

Then inside becomes

-\sqrt{3} + 9 + \sqrt{3} = 9

.

Finally,

\sqrt{9} = 3

.

Answer:

B. 3

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