Evaluate : $$\sqrt {20} + \sqrt {12} + \root 3 \of {729} \,\, - $$ $$\frac{4}{{\sqrt 5 - \sqrt 3 }} \,- $$ $$\sqrt {81} = ?$$
A. $$\sqrt 2 $$
B. $$\sqrt 3 $$
C. 0
D. $$2\sqrt 2 $$
Answer: Option C
Solution(By Examveda Team)
$$\sqrt {20} + \sqrt {12} + \root 3 \of {729} - \frac{4}{{\sqrt 5 - \sqrt 3 }} - \sqrt {81} $$$$ = 2\sqrt 5 + 2\sqrt 3 + 9\, - $$ $$\left( {\frac{4}{{\sqrt 5 - \sqrt 3 }} \times \frac{{\sqrt 5 + \sqrt 3 }}{{\sqrt 5 + \sqrt 3 }}} \right)$$ $$\, - \,9$$
$$\eqalign{ & = 2\sqrt 5 + 2\sqrt 3 + 9 - \left( {\frac{{4\left( {\sqrt 5 + \sqrt 3 } \right)}}{2}} \right) - 9 \cr & = 2\sqrt 5 + 2\sqrt 3 + 9 - 2\sqrt 5 - 2\sqrt 3 - 9 \cr & = 0 \cr} $$
Related Questions on Surds and Indices
A. $$\frac{1}{2}$$
B. 1
C. 2
D. $$\frac{7}{2}$$
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
A. 1.45
B. 1.88
C. 2.9
D. 3.7
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