# Spectrum Math Grade 8 Chapter 2 Lesson 7 Answer Key Comparing and Ordering Irrational Numbers

Students can use the Spectrum Math Grade 8 Answer Key Chapter 2 Lesson 2.7 Comparing and Ordering Irrational Numbers as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 2 Lesson 2.7 Comparing and Ordering Irrational Numbers Answers Key

Rational and irrational numbers can be compared by approximating their value and placing them along a number line.
Place these numbers on a number line: $$\sqrt{5}$$, 2.5, $$\sqrt{3}$$ Put the values below in order from least to greatest along a number line.

Question 1.
π2, 10, $$\sqrt{75}$$  Rational and irrational numbers can be compared by approximating their value and placing them along a number line.

Question 2.
$$\sqrt{7}$$, $$\frac{\sqrt{7}}{2}$$, 2  Rational and irrational numbers can be compared by approximating their value and placing them along a number line.

Question 3.
$$\sqrt{10}$$, 3.5, 22  Rational and irrational numbers can be compared by approximating their value and placing them along a number line.

Question 4.
4, $$\sqrt{15}$$, 5.2  Rational and irrational numbers can be compared by approximating their value and placing them along a number line.

Question 5.
$$\frac{1}{3}$$, $$\sqrt{1}$$, 0.45  Rational and irrational numbers can be compared by approximating their value and placing them along a number line.

Question 6.
$$\sqrt{72}$$, 9, 82  Rational and irrational numbers can be compared by approximating their value and placing them along a number line.

Expressions and equations containing irrational numbers can be approximated by testing values.

Compare using <, >, or =.

$$\sqrt{3}$$ + 5 ____ 3 + $$\sqrt{5}$$
$$\sqrt{3}$$ is between 1 and 2, so use 1.5.
$$\sqrt{5}$$ is between 2 and 3, so use 2.5.
(1.5) + 5 ____ 3 + (2.5)
6.5 > 5.5

Approximate the value of each expression and then compare using <, >, or =.

Question 1.
a. $$\sqrt{10}$$ + 2 _____ 10 + $$\sqrt{2}$$
Approximation: ____________
Answer: $$\sqrt{10}$$ + 2 < 10 + $$\sqrt{2}$$
$$\sqrt{10}$$ + 2 _____ 10 + $$\sqrt{2}$$
$$\sqrt{10}$$ is between 3 and 4, so use 3.5.
$$\sqrt{2}$$ is between 1 and 2, so use 1.5.
3.5 + 2 _________ 10 + 1.5
5.5 < 11.5

b. 4 + $$\sqrt{2}$$ _____ $$\sqrt{4}$$ + 2
Approximation: ____________
Answer: 4 + $$\sqrt{2}$$ > $$\sqrt{4}$$ + 2
4 + $$\sqrt{2}$$ _____ $$\sqrt{4}$$ + 2
$$\sqrt{2}$$ is between 1 and 2, so use 1.5.
$$\sqrt{4}$$ is 2.
4 + 1.5 _____2 + 2
5.5 > 4

Question 2.
a. 12 + $$\sqrt{6}$$ _____ $$\sqrt{12}$$ + 6
Approximation: ____________
Answer: 12 + $$\sqrt{6}$$ < $$\sqrt{12}$$ + 6
12 + $$\sqrt{6}$$ _____ $$\sqrt{12}$$ + 6
$$\sqrt{6}$$ is between 2 and 3, so use 2.5.
$$\sqrt{12}$$ is between 3 and 4, so use 3.5.
12 +2.5 _________ 3.5+6
14.5  < 9.5

b. $$\sqrt{8}$$ + 6 _____ 8 + $$\sqrt{6}$$
Approximation: ____________
Answer: $$\sqrt{8}$$ + 6 < 8 + $$\sqrt{6}$$
$$\sqrt{8}$$ + 6 _____ 8 + $$\sqrt{6}$$
$$\sqrt{8}$$ is 2.
$$\sqrt{6}$$ is 1 and 2, so use 1.5.
2 + 6 ______ 8+1.5
8 < 9.5

Question 3.
a. 15 + $$\sqrt{12}$$ _____ $$\sqrt{15}$$ + 12
Approximation: ____________
Answer: 15 + $$\sqrt{12}$$ > $$\sqrt{15}$$ + 12
15 + $$\sqrt{12}$$ _____ $$\sqrt{15}$$ + 12
$$\sqrt{12}$$ is between 3 and 4, so use 3.5.
$$\sqrt{15}$$ is between 3 and 4, so use 3.5.
15 + 3.5 ________ 3.5+12
18.5  > 15.5

b. $$\sqrt{7}$$ + 3 _____ 7 + $$\sqrt{3}$$
Approximation: ____________
Answer: $$\sqrt{7}$$ + 3 < 7 + $$\sqrt{3}$$
$$\sqrt{7}$$ + 3 _____ 7 + $$\sqrt{3}$$
$$\sqrt{7}$$ is between 2 and 3, so use 2.5.
$$\sqrt{3}$$ is between 1 and 2, so use 1.5.
2.5 + 3 ________ 7+1.5
5.5 <  8.5

Question 4.
a. 4 + $$\sqrt{7}$$ _____ $$\sqrt{4}$$ + 7
Approximation: ____________
Answer:  4 + $$\sqrt{7}$$ < $$\sqrt{4}$$ + 7
4 + $$\sqrt{7}$$ _____ $$\sqrt{4}$$ + 7
$$\sqrt{7}$$ is between 1 and 2, so use 1.5.
$$\sqrt{4}$$ is between 1 and 2, so use 1.5.
4 + 1.5 ________ 1.5 + 7
5.5  < 8.5

b. $$\sqrt{3}$$ + 5 _____ 3 + $$\sqrt{5}$$
Approximation: ____________
Answer: $$\sqrt{3}$$ + 5 > 3 + $$\sqrt{5}$$
$$\sqrt{3}$$ + 5 _____ 3 + $$\sqrt{5}$$
$$\sqrt{3}$$ is between 1 and 2, so use 1.5.
$$\sqrt{5}$$ is between 2 and 3, so use 2.5.
1.5 + 5 ________ 3 + 2.5
6.5 > 5.5

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