82.
Let $$a = \frac{1}{{2 - \sqrt 3 }} + \frac{1}{{3 - \sqrt 8 }} + \frac{1}{{4 - \sqrt {15} }}$$       then we have

83.
The simplest value of $$\frac{{3\sqrt 8 - 2\sqrt {12} + \sqrt {20} }}{{3\sqrt {18} - 2\sqrt {27} + \sqrt {45} }}{\text{is:}}$$

84.
What is the value of $$\frac{1}{{{{\left( {0.1} \right)}^2}}} + \frac{1}{{{{\left( {0.01} \right)}^2}}} + \frac{1}{{{{\left( {0.5} \right)}^2}}} + \frac{1}{{{{\left( {0.05} \right)}^2}}}$$

85.
$$\frac{{{6^2} + {7^2} + {8^2} + {9^2} + {{10}^2}}}{{\sqrt {7 + 4\sqrt 3 } - \sqrt {4 + 2\sqrt 3 } }}$$     is equal to

86.
The value of $$\left( {{x^{\frac{1}{3}}} + {x^{ - \frac{1}{3}}}} \right)\left( {{x^{\frac{2}{3}}} - 1 + {x^{ - \frac{2}{3}}}} \right){\text{is:}}$$

87.
If 4x = √5 + 2, then the value of $$\left( {x - \frac{1}{{16x}}} \right)$$  is

88.
The value of $$\frac{1}{{1 + \sqrt 2 }} + \frac{1}{{\sqrt 2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 + \sqrt 4 }} + \frac{1}{{\sqrt 4 + \sqrt 5 }} + \frac{1}{{\sqrt 5 + \sqrt 6 }} + \frac{1}{{\sqrt 6 + \sqrt 7 }} + \frac{1}{{\sqrt 7 + \sqrt 8 }} + \frac{1}{{\sqrt 8 + \sqrt 9 }}{\text{is:}}$$

89.
Which value among $$\sqrt {11} + \sqrt 5 ,\,\sqrt {14} + \sqrt 2 ,\,\sqrt 8 + \sqrt 8 $$      is the largest?

90.
If x, y are rational numbers and$$\frac{{5 + \sqrt {11} }}{{3 - 2\sqrt {11} }} = x + y\sqrt {11} .$$     The values of x and y are

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