# Spectrum Math Grade 8 Chapter 2 Lesson 5 Answer Key Comparing Rational and Irrational Numbers

Students can use the Spectrum Math Grade 8 Answer Key Chapter 2 Lesson 2.5 Comparing Rational and Irrational Numbers as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 2 Lesson 2.5 Comparing Rational and Irrational Numbers Answers Key

Compare rational and irrational numbers by using a best guess for irrational numbers. $$\sqrt{3}$$ < 2 This statement is true because $$\sqrt{3}$$ is between 1 and 2. 5 > $$\sqrt{20}$$ This statement is true because $$\sqrt{20}$$ is between 4 and 5.

Compare using <, >, or =.

Question 1.
a. $$\sqrt{9}$$ ______ π
Answer: $$\sqrt{9}$$< π
This statement is true because $$\sqrt{9}$$ is 3 and value of π is 3.14.

b. 4.5 _____ $$\sqrt{25}$$
Answer: 4.5 < $$\sqrt{25}$$
This statement is true because $$\sqrt{25}$$ is 5. As 4.5 is less than 5. Therefore 4.5 is less than $$\sqrt{25}$$ .

c. 3.9 _____ $$\sqrt{10}$$
Answer: 3.9 > $$\sqrt{10}$$
This statement is true because  $$\sqrt{10}$$ is 3.16. As 3.16 is less than 3.9. Therefore, 3.9 is greater than
$$\sqrt{10}$$.

Question 2.
a.
$$\sqrt{2}$$ _____ 1
Answer: $$\sqrt{2}$$ > 1
This statement is true because $$\sqrt{2}$$ is 1.414. As 1.414 is greater than 1. Therefore, $$\sqrt{2}$$ > 1

b.
$$3 \sqrt{\frac{8}{27}}$$ ____ $$\frac{2}{3}$$
Answer: $$3 \sqrt{\frac{8}{27}}$$ = $$\frac{2}{3}$$
This statement is true because $$3 \sqrt{\frac{8}{27}}$$ is  $$\frac{2}{3}$$. Thereore, $$3 \sqrt{\frac{8}{27}}$$ is equal to $$\frac{2}{3}$$

c. 1.1 ____ $$\sqrt{2}$$
Answer: 1.1 < $$\sqrt{2}$$
This statement is true because $$\sqrt{2}$$ is 1.414. As 1.414 is greater than 1. Therefore, 1.1 is less than $$\sqrt{2}$$.

Question 3.
a.
$$0 . \overline{66}$$ _____ $$\frac{2}{3}$$
Answer: $$0 . \overline{66}$$ = $$\frac{2}{3}$$
This statement is true because $$\frac{2}{3}$$ is $$0 . \overline{66}$$. Therefore, $$0 . \overline{66}$$ = $$\frac{2}{3}$$

b.
$$\sqrt{8}$$ _____ 3
Answer: $$\sqrt{8}$$ < 3
This statement is true because $$\sqrt{8}$$ is 2.82. As 2.82 is less than 3. Therefore, $$\sqrt{8}$$ is less than 3.

c.
1 ______ $$\sqrt{\frac{16}{25}}$$
Answer: 1 > $$\sqrt{\frac{16}{25}}$$
This statement is true because $$\sqrt{\frac{16}{25}}$$ is 0.8. As 1 is greater than 0.8. Therefore, 1 is greater than $$\sqrt{\frac{16}{25}}$$.

Question 4.
a. $$\sqrt{36}$$ ____ 6.5
Answer: $$\sqrt{36}$$ < 6.5
This statement is true because $$\sqrt{36}$$ is 6. As 6 is less than 6.5. Therefore, $$\sqrt{36}$$is less than 6.5.

b. 1 ____ $$0 . \overline{45}$$
Answer: 1 > $$0 . \overline{45}$$
This statement is true because 1 is always greater than $$0 . \overline{45}$$

c. $$\frac{3}{5}$$ _____ $$\sqrt{\frac{9}{5}}$$
Answer: $$\frac{3}{5}$$ < $$\sqrt{\frac{9}{5}}$$
This statement is true because $$\frac{3}{5}$$ is 0.6 and $$\sqrt{\frac{9}{5}}$$ is 1.34. As 1.34 is greater than 0.6. Therefore, $$\frac{3}{5}$$ < $$\sqrt{\frac{9}{5}}$$

Question 5.
a.
$$\sqrt[3]{343}$$ ____ 7.2
Answer: $$\sqrt[3]{343}$$ < 7.2
this statement is true because $$\sqrt[3]{343}$$ is 7. As 7 is less than 7.2. Therefore, $$\sqrt[3]{343}$$ is less than 7.2.

b. $$0 . \overline{77}$$ ____ $$\frac{7}{9}$$
Answer: $$0 . \overline{77}$$ = $$\frac{7}{9}$$
This statement is true because $$\frac{7}{9}$$ is $$0 . \overline{77}$$. Therefore, $$0 . \overline{77}$$ = $$\frac{7}{9}$$

c. 7 _____ $$\sqrt{52}$$
Answer: 7 < $$\sqrt{52}$$
This statement is true because $$\sqrt{52}$$ is 7.2. As 7 is less than 7.2. Therefore, 7 is less than $$\sqrt{52}$$.

Question 6.
a. $$\sqrt{5}$$ ____ 4
Answer: $$\sqrt{5}$$ < 4
This statement is true because $$\sqrt{5}$$ is 2.23. As 2.23 is less than 4. Therefore, $$\sqrt{5}$$ is less than 4.

b. $$\frac{3}{4}$$ _____ $$0 . \overline{75}$$
Answer: $$\frac{3}{4}$$ < $$0 . \overline{75}$$
This statement is true because $$\frac{3}{4}$$ is 0.75. As 0.75 is less than $$0 . \overline{75}$$. Therefore, $$\frac{3}{4}$$ is less than $$0 . \overline{75}$$

c. ____ 3.5
This statement is true because is 3.17. As 3.17 is less than 3.5. Therefore, is less than 3.5.

Question 7.
a. $$\frac{5}{10}$$ _____ $$\sqrt{1}$$
Answer: $$\frac{5}{10}$$ <  $$\sqrt{1}$$
This statement is true because $$\frac{5}{10}$$ is 0.5  and  $$\sqrt{1}$$ is 1. As 0.5 is less than 1. Therefore, $$\frac{5}{10}$$ is less than $$\sqrt{1}$$.

b. $$\sqrt[3]{6}$$ ____ 2
Answer: $$\sqrt[3]{6}$$ < 2
This statement is true because $$\sqrt[3]{6}$$ is 0.5. As 0.5 is less than 2. Therefore, $$\sqrt[3]{6}$$ is less than 2.

c. 1.4 ____ $$\sqrt{2}$$
Answer: 1.4 = $$\sqrt{2}$$
This statement is true because $$\sqrt{2}$$ is 1.4. Therefore, 1.4 is equal to $$\sqrt{2}$$.

Question 8.
a.
$$\sqrt[3]{\frac{27}{125}}$$ ____ 0.6
Answer: $$\sqrt[3]{\frac{27}{125}}$$  = 0.6
This statement is true because $$\sqrt[3]{\frac{27}{125}}$$  is 0.6. Therefore $$\sqrt[3]{\frac{27}{125}}$$  is equal to 0.6.

b.
$$\frac{1}{2}$$ ____ 0.55
Answer: $$\frac{1}{2}$$  < 0.55
This statement is true because $$\frac{1}{2}$$  is 0.5. As 0.5 is less than 0.55. Therefore, $$\frac{1}{2}$$  is less than 0.55.

c.
$$\sqrt[3]{18}$$ ____ 2.5
Answer: $$\sqrt[3]{18}$$ < 2.5
This statement is true because $$\sqrt[3]{18}$$ is 0.408. As 0.408 is less than 2.5. Therefore, $$\sqrt[3]{18}$$ is less than 2.5

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