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.