Question 175
Um cubo tem aresta de 3 cm. A diagonal do cubo, em cm, é
(A) $3\sqrt{2}$ (B) $3\sqrt{3}$ (C) $6\sqrt{2}$ (D) $6\sqrt{3}$ (E) $9\sqrt{2}$

QUESTION 175
The value of $\sqrt{144} + \sqrt{25}$ is
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21

Exercise I

I-A- $\quad \frac { ( 2 \sqrt { 3 } ) ^ { 2 } \times 12 ^ { 3 } \times 3 ^ { 2 } } { 3 ^ { - 4 } \times ( \sqrt { 2 } ) ^ { 4 } } = 3 ^ { 10 } \times 2 ^ { 8 }$. I-B- $\quad 2 \sqrt { 27 } - ( 2 \sqrt { 3 } - 1 ) ^ { 2 } = 10 \sqrt { 3 } - 13$. I-C- $\quad \ln \left( \frac { e } { 4 } \right) + \ln \left( \frac { 1 } { 9 e } \right) + \ln ( 36 e ) = 1$. I-D- $\quad e ^ { 2 \ln 3 + \ln 5 } + e ^ { - 2 \ln 5 } = 20$. I-E- For every real number $x$ different from $-2$ and from $2$, $\frac { 2 } { x + 2 } - \frac { 1 } { x - 2 } + \frac { 8 } { x ^ { 2 } - 4 } = \frac { 1 } { x - 2 }$. I-F- For every real number $x$, $\frac { e ^ { 2 x } + 2 e ^ { x } + 1 } { e ^ { x } + 1 } = e ^ { x } + 1$.
For each statement, indicate whether it is TRUE or FALSE.

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

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

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

$$\frac { \sqrt { 48 } } { \frac { 1 } { \sqrt { 3 } } + \frac { 1 } { \sqrt { 27 } } }$$
What is the result of this operation?
A) 3
B) 5
C) 8
D) 9
E) 12

$$\frac { \sqrt { 12 } } { \sqrt { 27 } + \frac { 1 } { \sqrt { 3 } } }$$
What is the result of this operation?
A) $\frac { 2 } { 3 }$
B) $\frac { 3 } { 5 }$
C) $\frac { 1 } { 2 }$
D) $\sqrt { 3 }$
E) $\sqrt { 6 }$

$\frac { \sqrt { 48 } + \sqrt { 75 } } { \sqrt { 108 } - \sqrt { 27 } }$\ What is the result of this operation?\ A) 1\ B) 2\ C) 3\ D) 4\ E) 5

$$\sqrt [ 3 ] { \frac { 32 } { \sqrt { 8 } - \sqrt { 2 } } }$$
What is the result of this operation?
A) $\sqrt { 2 }$ B) $2 \sqrt { 2 }$ C) $\sqrt [ 3 ] { 2 }$ D) 2 E) 4

When the numbers $\sqrt{5}, \sqrt{8}, \sqrt{12}, \sqrt{18}, \sqrt{20}$ and $\sqrt{27}$ are placed in the boxes below, with each box containing a different number, A, B, and C become whole numbers.
Accordingly, what is the sum $\mathrm{A} + \mathrm{B} + \mathrm{C}$?
A) 40
B) 44
C) 48
D) 52
E) 56

Mert, who performs operations with radical numbers, instead of multiplying the number $\sqrt{10} + \sqrt{6}$ by its conjugate $\sqrt{10} - \sqrt{6}$, mistakenly divided it.
Accordingly, how much greater is the number Mert found than the number he should have found?
A) $\sqrt{12}$ B) $\sqrt{15}$ C) $\sqrt{18}$ D) $\sqrt{20}$ E) $\sqrt{30}$

In a page of a mathematics textbook shown partially below, the result of the 1st operation is 12 more than the result of the 2nd operation.
$a = 2 \quad b = $
For the real numbers $a$ and $b$ given above, find the result of the following operations.
1. operation: $a\sqrt{b} + \sqrt{b} = $ 2. operation: $a\sqrt{b} - \sqrt{b} = $ 3. operation: $a\sqrt{b} \times \sqrt{b} = $ 4. operation: $a\sqrt{b} \div \sqrt{b} = $
Accordingly, the result of the 3rd operation is equal to how many times the result of the 4th operation?
A) 9 B) 16 C) 24 D) 30 E) 36