(1) Choose the correct answer from the given options:

1

Which of the following numbers is an irrational number?

(a) $0.\bar{3}$
(b) $\sqrt{9/25}$
(c) $\sqrt{5}$
(d) $\sqrt[3]{-125}$
2

What is the estimate of $\sqrt{41}$ to the nearest integer?

(a) $6$
(b) $7$
(c) $36$
(d) $49$
3

Which of the following numbers is an irrational number that lies between 2 and 3?

(a) $2.5$
(b) $1/3$
(c) $6.25$
(d) $\sqrt[3]{9}$
4

If $X < \sqrt{29} < X+1, X \in \mathbb{Z}$, what is the value of $X$?

(a) $4$
(b) $5$
(c) $6$
(d) $7$
5

What is the estimate of $\sqrt[3]{25}$ to the nearest integer?

(a) $2$
(b) $3$
(c) $5$
(d) $12.5$
6

If $1 < \sqrt{n} < 2$, which of the following is a possible value for n?

(a) $1$
(b) $2$
(c) $4$
(d) $8$

Section Two: Find the solution set in $\mathbb{R}$ for each of the following equations:

1

$x^3 - 11 = 5$

2

$2x^3 + 13 = 67$

3

$\frac{2}{3}x^2 = \frac{4}{15}$

4

$3x^2 - 1 = -13$

Section Three: Find the solution set in $\mathbb{Q}$ for each of the following equations:

1

$2x^2 - 3 = 9$

2

$6x^2 - 3 = 4x^2 + 7$

3

$2(x^3 + 1) = 18$

Answer Key

Note: Solutions are not automatically generated by the model. Please solve the problems manually to check your answers.