Question

1. $\sqrt{50}$
2. $\sqrt{180}$
3. $2\sqrt{72}$
4. $2\sqrt{32}$
5. $-2\sqrt{108}$
6. $6\sqrt{28}$
7. the expression $\sqrt{200}$ is equivalent to

a. $25\sqrt{8}$
b. $100\sqrt{2}$
c. $2\sqrt{10}$
d. $10\sqrt{2}$

1. which is equivalent to $4\sqrt{3}$?

a. 144
b. $\sqrt{48}$
c. $\sqrt{19}$
d. $\sqrt{16}$

1. the expression $2\sqrt{5}$ is equivalent to

a. $\sqrt{10}$
b. $\sqrt{20}$
c. $\sqrt{50}$
d. $\sqrt{100}$

1. which is equivalent to $\sqrt{40}$?

a. $2\sqrt{10}$
b. $2\sqrt{20}$
c. $4\sqrt{10}$
d. $10\sqrt{2}$

1. the expression $\sqrt{500}$ is equivalent to

a. $5\sqrt{10}$
b. $10\sqrt{5}$
c. $500\sqrt{2}$
d. $5\sqrt{100}$

1. when $\sqrt{72}$ is expressed in simplest $a\sqrt{b}$ form, what is the value of $a$?

a. 6
b. 2
c. 3
d. 8

Explanation:

Step1: Simplify $\sqrt{50}$

Factor into perfect square: $\sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$

Step2: Simplify $\sqrt{180}$

Factor into perfect square: $\sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5} = 6\sqrt{5}$

Step3: Simplify $2\sqrt{72}$

Factor into perfect square: $2\sqrt{36 \times 2} = 2 \times \sqrt{36} \times \sqrt{2} = 2 \times 6\sqrt{2} = 12\sqrt{2}$

Step4: Simplify $2\sqrt{32}$

Factor into perfect square: $2\sqrt{16 \times 2} = 2 \times \sqrt{16} \times \sqrt{2} = 2 \times 4\sqrt{2} = 8\sqrt{2}$

Step5: Simplify $-2\sqrt{108}$

Factor into perfect square: $-2\sqrt{36 \times 3} = -2 \times \sqrt{36} \times \sqrt{3} = -2 \times 6\sqrt{3} = -12\sqrt{3}$

Step6: Simplify $6\sqrt{28}$

Factor into perfect square: $6\sqrt{4 \times 7} = 6 \times \sqrt{4} \times \sqrt{7} = 6 \times 2\sqrt{7} = 12\sqrt{7}$

Step7: Solve Q11: $\sqrt{200}$

Factor into perfect square: $\sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2} = 10\sqrt{2}$

Step8: Solve Q12: Match $4\sqrt{3}$

Convert to single radical: $\sqrt{16 \times 3} = \sqrt{48}$

Step9: Solve Q13: Match $2\sqrt{5}$

Convert to single radical: $\sqrt{4 \times 5} = \sqrt{20}$

Step10: Solve Q14: Simplify $\sqrt{40}$

Factor into perfect square: $\sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}$

Step11: Solve Q15: Simplify $\sqrt{500}$

Factor into perfect square: $\sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10\sqrt{5}$

Step12: Solve Q16: Simplify $\sqrt{72}$

Factor into perfect square: $\sqrt{36 \times 2} = 6\sqrt{2}$, so $a=6$

Answer:

1. $5\sqrt{2}$
2. $6\sqrt{5}$
3. $12\sqrt{2}$
4. $8\sqrt{2}$
5. $-12\sqrt{3}$
6. $12\sqrt{7}$
7. d. $10\sqrt{2}$
8. b. $\sqrt{48}$
9. b. $\sqrt{20}$
10. a. $2\sqrt{10}$
11. b. $10\sqrt{5}$
12. a. 6