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If \(x = \sqrt {-\sqrt 3 + \sqrt {3 + 8\sqrt {7 + 4\sqrt 3}}}\) where x > 0, then the value of x is equal to:
1. 1
2. 2
3. 4
4. 3

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Correct Answer - Option 2 : 2

Given:

\(x = \sqrt { - \sqrt 3 + \sqrt {3 + 8\sqrt {7 + 4\sqrt 3 } } } \)

Concept used:

(a + b)2 = a2 + b2 + 2ab

Calculation:

\(x = \sqrt { - \sqrt 3 + \sqrt {3 + 8\sqrt {4 + 3 + 4\sqrt 3 } } } \)

 \(x = \sqrt { - \sqrt 3 + \sqrt {3 + 8\sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} } } \)

\(x = \sqrt { - \sqrt 3 + \sqrt {3 + \sqrt {8\left( {2 + \sqrt 3 } \right)} } } \)

\(x = \sqrt { - \sqrt 3 + \sqrt {3 + 16 + 8\sqrt 3 } } \)

\(x = \sqrt { - \sqrt 3 + \sqrt {{{\left( {4 + \sqrt 3 } \right)}^2}} } \)

\(x = \sqrt { - \sqrt 3 + 4 + \sqrt 3 } \)

\(x = \sqrt 4 \)

So, The value of x is '2'

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