If $$a= {7-4\sqrt{3} }$$
find the value of $$\sqrt{a} +\dfrac{1}{\sqrt{a} } $$

Question

If $$a= {7-4\sqrt{3}   }$$  
​ find the value of  $$\sqrt{a} +\dfrac{1}{\sqrt{a}  }  $$

Uniteasy Admin · Accepted Answer

$$a= {7-4\sqrt{3}   } $$
$$=2^2-4\sqrt{3}+(\sqrt{3}  )^2  $$
$$=(2-\sqrt{3})^2  $$
Therefore
$$\sqrt{a}  =2-\sqrt{3}  $$
Reciprocal of $$\sqrt{a}$$  
$$\dfrac{1}{\sqrt{a}  }=\dfrac{1}{2-\sqrt{3}  }  $$
$$=\dfrac{1}{2-\sqrt{3} }  \cdot \dfrac{2+\sqrt{3}}{2+\sqrt{3}  }  $$
$$=2+\sqrt{3} $$ 
Addition of $$\sqrt{a}$$ and $$\dfrac{1}{\sqrt{a}  }   $$ 
$$\sqrt{a} +\dfrac{1}{\sqrt{a}  }   = 4$$
So option A is the right choice

Multiple Choice Question (MCQ)

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