Select the value of $1 . \overline { 5 } \times 5$.
(1) $7 . \overline { 5 }$
(2) $7 . \overline { 6 }$
(3) $7 . \overline { 7 }$
(4) $7 . \overline { 8 }$
(5) $7 . \overline { 9 }$

16. Given that $c$ and $d$ are non-zero integers, the expression $\frac { 10 ^ { c - 2 d } \times 20 ^ { 2 c + d } } { 8 ^ { c } \times 125 ^ { c + d } }$ is an integer if
A $\quad c < 0$
B $\quad d < 0$
C $\quad c < 0$ and $d < 0$
D $\quad c < 0$ and $d > 0$
E $\quad c > 0$ and $d < 0$
F $\quad c > 0$ and $d > 0$ G $\quad d > 0$
H $\quad c > 0$

Find the value of the expression
$$\sqrt { 8 - 4 \sqrt { 2 } + 1 } + \sqrt { 9 - 12 \sqrt { 2 } + 8 }$$

Given that
$$\frac { 1 } { \sqrt { x } - 6 } - \frac { 1 } { \sqrt { x } + 6 } = \frac { 3 } { 11 }$$
what is the value of $x$ ?
A $2 \sqrt { 15 }$ B $4 \sqrt { 5 }$ C $5 \sqrt { 2 }$ D $\sqrt { 58 }$ E 50 F 58 G 60 H 80

$$\frac { 6 } { \sqrt { 3 } } - \frac { 2 } { \sqrt { 3 } + 1 }$$
What is the result of this operation?
A) $\sqrt { 3 }$
B) $2 \sqrt { 3 }$
C) $\sqrt { 3 } - 1$
D) $\sqrt { 3 } + 1$
E) $2 \sqrt { 3 } - 1$

$10 ^ { -1 } + 10 ^ { -2 } + 10 ^ { -3 }$
What is the result of this operation?
A) 0,011
B) 0,101
C) 0,111
D) 0,123
E) 0,321

$( 16 ) ^ { 3 n } = 8 ^ { 5 }$
Given this, what is n?
A) $\frac { 3 } { 2 }$
B) $\frac { 4 } { 3 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 5 } { 4 }$
E) $\frac { 5 } { 6 }$

Which of the following is a rational number?
A) $\sqrt { 2 } + 1$
B) $2 \sqrt { 2 } - 1$
C) $\frac { 1 } { \sqrt { 2 } }$
D) $\frac { \sqrt { 2 } } { \sqrt { 2 } + 1 }$
E) $\frac { 2 \sqrt { 2 } - 2 } { 3 \sqrt { 2 } - 3 }$

$$\frac { 3 } { 0,2 } - ( 0,25 ) ^ { - 2 }$$
What is the result of this operation?
A) $\frac { - 2 } { 5 }$
B) $\frac { 3 } { 10 }$
C) $\frac { 1 } { 15 }$
D) - 1
E) - 3

$\frac { 4 ^ { \frac { 1 } { 2 } } + ( - 8 ) ^ { \frac { 1 } { 3 } } - 1 } { 2 ^ { - 1 } }$
What is the result of this operation?
A) 2 B) 6 C) $-1$ D) 0 E) $-2$

$x = \sqrt[3]{4}$
$$y = \sqrt[4]{8}$$ $$z = \sqrt[5]{16}$$
Given that, which of the following orderings is correct?
A) $x < y < z$ B) $x < z < y$ C) $y < x < z$ D) $z < x < y$ E) $z < y < x$

$$\frac { 16 ^ { 3 } } { 24 ^ { 3 } + 16 ^ { 3 } + 8 ^ { 3 } }$$
What is the result of this operation?
A) $\frac { 1 } { 3 }$
B) $\frac { 3 } { 4 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 4 } { 7 }$
E) $\frac { 2 } { 9 }$

$$\frac { 6 ^ { -2 } - 4 \cdot 6 ^ { -3 } } { 3 ^ { -2 } - 2 \cdot 3 ^ { -3 } }$$
What is the result of this operation?
A) $\frac { 1 } { 3 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 1 } { 4 }$

$$\begin{aligned} & a = \sqrt { 12 } - \sqrt { 8 } \\ & b = \sqrt { 27 } + \sqrt { 18 } \end{aligned}$$
Given that, what is the product a.b?
A) $4 \sqrt { 2 }$
B) $3 \sqrt { 3 }$
C) 4
D) 5
E) 6

Given that $x = \sqrt [ 4 ] { 5 }$,
$$\left( x ^ { 2 } - 2 \right) ^ { - 1 }$$
which of the following is this expression equal to?
A) $1 + \sqrt [ 4 ] { 5 }$
B) $2 + \sqrt [ 4 ] { 5 }$
C) $1 + \sqrt { 5 }$
D) $2 + \sqrt { 5 }$
E) $1 + 2 \sqrt { 5 }$

$$\left( 1 - 3 ^ { - 1 } + a ^ { - 1 } \right) ^ { - 3 } = 8$$
Given this, what is a?
A) $- 6$
B) $- 4$
C) $\frac { - 2 } { 3 }$
D) $\frac { 3 } { 4 }$
E) $\frac { 1 } { 6 }$

$$\frac { 2 ^ { - 2 } } { 4 ^ { - 1 } + \frac { 1 } { m ^ { - 1 } } } = 13 ^ { - 1 }$$
Given this, what is m?
A) 3
B) 4
C) 5
D) 6
E) 7

$$2 \cdot ( 0,2 ) ^ { 3 } + ( 0,4 ) ^ { 3 }$$
What is the result of this operation?
A) 0,06
B) 0,08
C) 0,1
D) 0,12
E) 0,14

$$\frac { 1 + \sqrt { a } } { 1 - a } - \frac { a } { 1 - \sqrt { a } } = \frac { 5 } { 3 }$$
Given this, what is a?
A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 9 }$
E) $\frac { 4 } { 9 }$

$$\left[ \left( \frac { - 1 } { 2 } \right) ^ { - 2 } \right] ^ { 3 }$$
What is the result of this operation?
A) - 32
B) - 16
C) 12
D) 32
E) 64

$6 ^ { - 3 } \left( 8 ^ { 3 } - 6 ^ { 3 } + 4 ^ { 3 } \right)$ What is the result of this operation?
A) $\frac { 1 } { 2 }$
B) $\frac { 4 } { 3 }$
C) $\frac { 5 } { 3 }$
D) $\frac { 9 } { 4 }$
E) $\frac { 5 } { 6 }$

For a real number $\mathbf { x }$,
$$\sqrt { \frac { \sqrt { x } + 2 } { \sqrt { x } - 2 } } = \sqrt { x } + 2$$
Given that, what is x?
A) 3
B) 4
C) 5
D) 6
E) 7

Given that $x \neq - 1$ and
$$( x + 1 ) \sqrt { x - 1 } = \sqrt { 2 x + 2 }$$
What is $x$?
A) $\frac { 3 \sqrt { 3 } } { 2 }$
B) $\frac { 2 \sqrt { 3 } } { 3 }$
C) $\frac { 4 \sqrt { 2 } } { 3 }$
D) $\sqrt { 2 }$
E) $\sqrt { 3 }$

$$3 ^ { 2 } \cdot \frac { 1 - 3 ^ { - 4 } } { 1 - 3 ^ { - 2 } }$$
What is the result of this operation?
A) 4
B) 5
C) 8
D) 9
E) 10

$$\frac { \sqrt [ 3 ] { 2 \cdot \sqrt { 54 } } } { \sqrt { 2 } }$$
What is the result of this operation?
A) $\sqrt { 2 }$ B) $\sqrt { 3 }$ C) $\sqrt { 6 }$ D) $\sqrt [ 3 ] { 4 }$ E) $\sqrt [ 3 ] { 9 }$