71. $$2 + \frac{6}{{\sqrt 3 }} + \frac{1}{{2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 - 2}}$$ equals to
72. The simplified value of the following expression is:
$$\frac{1}{{\sqrt {11 - 2\sqrt {30} } }} - \frac{3}{{\sqrt {7 - 2\sqrt {10} } }} - \frac{4}{{\sqrt {8 + 4\sqrt 3 } }}$$
$$\frac{1}{{\sqrt {11 - 2\sqrt {30} } }} - \frac{3}{{\sqrt {7 - 2\sqrt {10} } }} - \frac{4}{{\sqrt {8 + 4\sqrt 3 } }}$$
73. Which value among $$\root 4 \of 7 ,\,\root 3 \of {11} $$ and $$\root {12} \of {1257} $$ is the largest?
74. If $$\frac{{4 + 3\sqrt 3 }}{{\sqrt {7 + 4\sqrt 3 } }} = {\text{A}} + \sqrt {\text{B}} ,$$ then B - A is
75. The Simplified value of $$\frac{{\sqrt 6 + 2}}{{\sqrt 2 + \sqrt {2 + \sqrt 3 } }} - \frac{{\sqrt 6 - 2}}{{\sqrt 2 - \sqrt {2 - \sqrt 3 } }} - \frac{{2\sqrt 2 }}{{2 + \sqrt 2 }}$$
76. What is the value of $$\frac{1}{{0.2}} + \frac{1}{{0.02}} + \frac{1}{{0.002}} + \,.....$$ upto 9 terms?
77. $$\eqalign{
& {\text{If m}} = \sqrt {5 + \sqrt {5 + \sqrt {5\,......} } } \cr
& {\text{n}} = \sqrt {5 - \sqrt {5 - \sqrt {5\,......} } } \cr} $$
then among the following the relation between m & n holds is.
then among the following the relation between m & n holds is.
78. What is the value of x in the equation $$\sqrt {\frac{{1 + x}}{x}} - \sqrt {\frac{x}{{1 + x}}} = \frac{1}{{\sqrt 6 }}?$$
79. The simplified value of $$\left( {\sqrt 6 + \sqrt {10} - \sqrt {21} - \sqrt {35} } \right)\left( {\sqrt 6 - \sqrt {10} + \sqrt {21} - \sqrt {35} } \right){\text{is}}$$
80. The value of $$\frac{1}{{1 + \sqrt 2 + \sqrt 3 }} + \frac{1}{{1 - \sqrt 2 + \sqrt 3 }}\,{\text{is:}}$$
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