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Evaluate : $$\sqrt {20} + \sqrt {12} + \root 3 \of {729} \,\, - $$     $$\frac{4}{{\sqrt 5 - \sqrt 3 }} \,- $$   $$\sqrt {81} = ?$$

Evaluate : $$\sqrt {20} + \sqrt {12} + \root 3 \of {729} \,\, - $$     $$\frac{4}{{\sqrt 5 - \sqrt 3 }} \,- $$   $$\sqrt {81} = ?$$ Correct Answer 0

$$\sqrt {20} + \sqrt {12} + \root 3 \of {729} - \frac{4}{{\sqrt 5 - \sqrt 3 }} - \sqrt {81} $$
$$ = 2\sqrt 5 + 2\sqrt 3 + 9\, - $$   $$\left( {\frac{4}{{\sqrt 5 - \sqrt 3 }} \times \frac{{\sqrt 5 + \sqrt 3 }}{{\sqrt 5 + \sqrt 3 }}} \right)$$     $$\, - \,9$$
$$\eqalign{ & = 2\sqrt 5 + 2\sqrt 3 + 9 - \left( {\frac{{4\left( {\sqrt 5 + \sqrt 3 } \right)}}{2}} \right) - 9 \cr & = 2\sqrt 5 + 2\sqrt 3 + 9 - 2\sqrt 5 - 2\sqrt 3 - 9 \cr & = 0 \cr} $$

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