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

1

What is the value of $\sqrt{18} + \sqrt{32}$?

(a) $7\sqrt{2}$
(b) $\sqrt{50}$
(c) $5\sqrt{4}$
(d) $7\sqrt{4}$
2

Which of the following is true?

(a) $\sqrt{40} = 4\sqrt{10}$
(b) $\sqrt{32} = 8\sqrt{2}$
(c) $\sqrt{12} = 2\sqrt{3}$
(d) $\sqrt{48} = 3\sqrt{6}$
3

Which of the following is equivalent to $3\sqrt{5} \times \sqrt{25}$?

(a) $3\sqrt{30}$
(b) $5\sqrt{3}$
(c) $125$
(d) $5\sqrt{5}$
4

Which of the following is equivalent to $\sqrt{\frac{72}{2}}$?

(a) $2\sqrt{6}$
(b) $6\sqrt{2}$
(c) $6$
(d) $\sqrt{70}$
5

Which of the following is equivalent to $\sqrt{\frac{25}{15}}$?

(a) $\frac{\sqrt{5}}{3}$
(b) $ \frac{5}{3}$
(c) $\frac{\sqrt{15}}{3}$
(d) $\frac{5}{\sqrt{15}}$
6

If $x\sqrt{10} = \sqrt{160}$, what is the value of $x$?

(a) $3$
(b) $8$
(c) $4$
(d) $5$
7

If $\frac{\sqrt[3]{2}}{\sqrt[3]{a}} = \frac{\sqrt[3]{3}}{10} \times \sqrt[3]{a}$, what is the value of $a$?

(a) $15$
(b) $30$
(c) $\frac{3}{15}$
(d) $\frac{2}{15}$
8

If $2\sqrt{3} \times 4\sqrt{a} = 8\sqrt{6}$, what is the value of $a$?

(a) $\sqrt{2}$
(b) $2$
(c) $\sqrt{6}$
(d) $2\sqrt{6}$
9

If $\frac{\sqrt{3}}{\sqrt{a}} = \frac{\sqrt{2}}{\sqrt{6}}$, what is the value of $a$?

(a) $3\sqrt{3}$
(b) $3$
(c) $\sqrt{6}$
(d) $9$
10

If $x + \sqrt{28} = \sqrt{7}$, what is the value of $x$?

(a) $\sqrt{21}$
(b) $-\sqrt{21}$
(c) $\sqrt{7}$
(d) $-\sqrt{7}$

Section Two: Applying Concepts

(1) Simplify each of the following to its simplest form:

1

$3\sqrt{1} - \sqrt{27}$

2

$2\frac{3}{1} + \sqrt{\frac{3}{16}}$

3

$2\frac{\sqrt[3]{5}}{\sqrt[3]{10}} \times \sqrt[3]{54}$

4

$\sqrt{\frac{98}{8}} + \sqrt{8}$

5

$3\sqrt[3]{32} - 3\sqrt[3]{4}$

6

$3\sqrt{8} + \sqrt{18} - \sqrt{32}$

7

$\sqrt{48} + \frac{4}{3}\sqrt{27} + \sqrt{75}$

8

$\sqrt{192} - 3\sqrt{75} + 2\sqrt{24}$

9

$\frac{3}{2}\sqrt{256} + \frac{12}{\sqrt{16}} + \sqrt{32}$

(2) In each of the following, find the value of $x$:

1

$x\sqrt{32} = 2\sqrt{50} + \sqrt{72}$

2

$x\sqrt[3]{10} = \sqrt[3]{80} - \sqrt[3]{270}$

Answer Key

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