# Spectrum Math Grade 8 Chapter 2 Lesson 6 Answer Key Approximating Irrational Numbers

Students can use the Spectrum Math Grade 8 Answer Key Chapter 2 Lesson 2.6 Approximating Irrational Numbers as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 2 Lesson 2.6 Approximating Irrational Numbers Answers Key

Approximate the value of an irrational number by exploring values.
The value of $$\sqrt{2}$$ is something between 1 and 2.
Look at the squares of 1.4 and 1.5.
1.42 = 1.96
1.52 = 2.25
By looking at these squares, it is evident that $$\sqrt{2}$$ is between 1.4 and 1.5.

Approximate the value of each root to the tenths place.

Question 1.
The value of $$\sqrt{7}$$ is between ____ and _____
Answer: The value of $$\sqrt{7}$$ is something between 2 and 3.
Look at the squares of 2.6 and 2.7.
2.62 = 6.76
2.72 = 7.29
By looking at these squares, it is evident that $$\sqrt{7}$$ is between 2.6 and 2.7.

Question 2.
The value of $$\sqrt{10}$$ is between ___ and _____
Answer: The value of $$\sqrt{10}$$ is something between 3 and 4.
Look at the squares of 3.1 and 3.2.
3.12 = 9.61
3.22 = 10.24
By looking at these squares, it is evident that $$\sqrt{2}$$ is between 3.1 and 3.2.

Question 3.
The value of $$\sqrt{26}$$ is between ____ and _____
Answer: The value of $$\sqrt{26}$$ is something between 5 and 6.
Look at the squares of 5 and 5.1.
52 = 25
5.12 = 26.01
By looking at these squares, it is evident that $$\sqrt{26}$$ is between 5 and 5.1.

Question 4.
The value of $$\sqrt[3]{25}$$ is between ____ and _____
Answer: The value of $$\sqrt[3]{25}$$ is something between 2 and 3.
Look at the squares of 2.7 and 2.8.
2.73 = 19.683
2.83 = 21.952
By looking at these squares, it is evident that $$\sqrt[3]{25}$$ is between 2.7 and 2.8.

Question 5.
The value of $$\sqrt[3]{99}$$ is between ____ and ____
Answer: The value of $$\sqrt[3]{99}$$ is something between 4 and 5.
Look at the squares of 4.6 and 4.7.
4.63 = 97.336
4.73 = 103.823
By looking at these squares, it is evident that $$\sqrt[3]{99}$$ is between 4.6 and 4.7.

Question 6.
The value of $$\sqrt[3]{514}$$ is between ___ and _____
Answer: The value of $$\sqrt[3]{514}$$ is something between 8 and 9.
Look at the squares of 8 and 8.1.
83 = 512
8.13 = 531.441
By looking at these squares, it is evident that $$\sqrt[3]{514}$$ is between 8 and 8.1.

Question 7.
The value of $$\sqrt{78}$$ is between ____ and ____
Answer: The value of $$\sqrt{78}$$ is something between 8 and 9.
Look at the squares of 8.8 and 8.9.
8.82 = 77.44
8.92 = 79.21
By looking at these squares, it is evident that $$\sqrt{78}$$ is between 8.8 and 8.9.

Question 8.
The value of $$\sqrt[3]{824}$$ is between ___ and ____
Answer: The value of $$\sqrt[3]{824}$$ is something between 9  and 10.
Look at the squares of 9.3 and 9.4.
9.33 = 804.357
9.43 = 830.584
By looking at these squares, it is evident that $$\sqrt[3]{824}$$ is between 9.3 and 9.4.

You can approximate the value of an irrational number to the hundredths place as well.

The value of $$\sqrt{3}$$ is something between 1 and 2.
Look at the squares of 1.7 and 1.8.
1.72 = 2.89
1.82 = 3.24
By looking at these squares, it is evident that $$\sqrt{3}$$ is between 1.7 and 1.8.

Now, narrow explore to the hundredths place.
1.732= 2.99
1.7142 = 3.03
By looking at these squares, it is evident that $$\sqrt{3}$$ is between 1.73 and 1.74.

Approximate each value to the hundredths place.

Question 1.
The value of $$\sqrt{8}$$ is between ___ and ____
Answer: The value of $$\sqrt{8}$$ is something between 2 and 3.
Look at the squares of 2.8 and 2.9.
2.82 = 7.84
2.92 = 8.41
By looking at these squares, it is evident that $$\sqrt{8}$$ is between 2.8 and 2.9.

Question 2.
The value of $$\sqrt{11}$$ is between ____ and ____
Answer: The value of $$\sqrt{11}$$ is something between 3 and 4.
Look at the squares of 3.3 and 3.4.
3.32 = 10.89
3.42 = 11.56
By looking at these squares, it is evident that $$\sqrt{11}$$ is between 3.3 and 3.4.

Question 3.
The value of $$\sqrt{90}$$ is between ____ and ____
Answer: The value of $$\sqrt{90}$$ is something between 9 and 100.
Look at the squares of 9.4 and 9.5.
9.42 = 88.36
9.52 = 90.25
By looking at these squares, it is evident that $$\sqrt{90}$$ is between 9.4 and 9.5.

Question 4.
The value of $$\sqrt[3]{72}$$ is between ____ and ____
Answer: The value of $$\sqrt[3]{72}$$ is something between 4  and 5.
Look at the squares of 4.1 and 4.2.
4.13 = 68.921
4.23 = 74.088
By looking at these squares, it is evident that $$\sqrt[3]{72}$$ is between 4.1 and 4.2.

Question 5.
The value of $$\sqrt[3]{81}$$ is between ____ and ____
Answer: The value of $$\sqrt[3]{81}$$ is something between 4  and 5.
Look at the squares of 4.3 and 4.4.
4.33 = 79.507
4.43 = 85.184
By looking at these squares, it is evident that $$\sqrt[3]{81}$$ is between 4.3 and 4.4.

Question 6.
The value of $$\sqrt{27}$$ is between ____ and ____
Answer: The value of $$\sqrt{27}$$ is something between 5 and 6.
Look at the squares of 5.1 and 5.2.
5.12 = 26.01
5.22 = 27.04
By looking at these squares, it is evident that $$\sqrt{27}$$ is between 5.1 and 5.2.

Question 7.
The value of $$\sqrt[3]{33}$$ is between ____ and ____
Answer: The value of $$\sqrt[3]{33}$$ is something between 3  and 4.
Look at the squares of 3.2 and 3.3.
3.23 = 32.768
3.33 = 35.937
By looking at these squares, it is evident that $$\sqrt[3]{33}$$ is between 3.2 and 3.3.

Question 8.
The value of $$\sqrt{23}$$ is between ____ and _____
Answer: The value of $$\sqrt{23}$$ is something between 4 and 5.
Look at the squares of 4.7 and 4.8.
4.72 = 22.09
4.82 = 23.09
By looking at these squares, it is evident that $$\sqrt{90}$$ is between 4.7 and 4.8.

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