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'