Related Topics:

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, solutions, and videos to help Grade 8 students learn how to use rational approximations of irrational numbers to compare the size of irrational numbers and place irrational numbers in their approximate locations on a number line.

### New York State Common Core Math Grade 8, Module 7, Lesson 13

• Students place irrational numbers in their approximate locations on a number line.

The decimal expansion of irrational numbers can be found using the method of rational approximation.

Lesson 13 Classwork

Opening Exercise

Exercises 1–11

1. Rodney thinks that \(\sqrt[3]{{64}}\) is greater than \(\frac{{17}}{4}\). Sam thinks that \(\frac{{17}}{4}\) is greater. Who is right and why?

2. Which number is smaller, \(\sqrt[3]{{27}}\) or 2.89? Explain.

3. Which number is smaller, \(\sqrt{{121}}\) or \(\sqrt[3]{{125}}\)? Explain.

4. Which number is smaller, \(\sqrt{{49}}\) or \(\sqrt[3]{{216}}\)? Explain.

5. Which number is greater, \(\sqrt{{50}}\) or \(\frac{{319}}{45}\)? Explain.

6. Which number is greater, \(\frac{{5}}{11}\) or \(0.\overline 4 \)? Explain.

7. Which number is greater, \(\sqrt{{38}}\) or \(\frac{{154}}{25}\)? Explain.

8. Which number is greater, \(\sqrt{{2}}\) or \(\frac{{15}}{9}\)? Explain.

9. Place the following numbers at their approximate location on the number line: \(\sqrt{25}\),\(\sqrt{28}\),\(\sqrt{30}\),\(\sqrt{32}\),\(\sqrt{35}\),\(\sqrt{36}\)

10. Challenge: Which number is larger \(\sqrt{5}\) or \(\sqrt[3]{11}\)?

11. A certain chessboard is being designed so that each square has an area of 3in^{2}. What is the length, rounded to the
tenths place, of one edge of the board? (A chessboard is composed of 64 squares as shown.)

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, solutions, and videos to help Grade 8 students learn how to use rational approximations of irrational numbers to compare the size of irrational numbers and place irrational numbers in their approximate locations on a number line.

Download Worksheets for Grade 8, Module 7, Lesson 13

Lesson 13 Student Outcomes

• Students use rational approximations of irrational numbers to compare the size of irrational numbers.• Students place irrational numbers in their approximate locations on a number line.

Lesson 13 Summary

The decimal expansion of rational numbers can be found by using long division, equivalent fractions, or the method of rational approximation.The decimal expansion of irrational numbers can be found using the method of rational approximation.

Lesson 13 Classwork

Opening Exercise

Exercises 1–11

1. Rodney thinks that \(\sqrt[3]{{64}}\) is greater than \(\frac{{17}}{4}\). Sam thinks that \(\frac{{17}}{4}\) is greater. Who is right and why?

2. Which number is smaller, \(\sqrt[3]{{27}}\) or 2.89? Explain.

3. Which number is smaller, \(\sqrt{{121}}\) or \(\sqrt[3]{{125}}\)? Explain.

4. Which number is smaller, \(\sqrt{{49}}\) or \(\sqrt[3]{{216}}\)? Explain.

5. Which number is greater, \(\sqrt{{50}}\) or \(\frac{{319}}{45}\)? Explain.

6. Which number is greater, \(\frac{{5}}{11}\) or \(0.\overline 4 \)? Explain.

7. Which number is greater, \(\sqrt{{38}}\) or \(\frac{{154}}{25}\)? Explain.

8. Which number is greater, \(\sqrt{{2}}\) or \(\frac{{15}}{9}\)? Explain.

9. Place the following numbers at their approximate location on the number line: \(\sqrt{25}\),\(\sqrt{28}\),\(\sqrt{30}\),\(\sqrt{32}\),\(\sqrt{35}\),\(\sqrt{36}\)

10. Challenge: Which number is larger \(\sqrt{5}\) or \(\sqrt[3]{11}\)?

11. A certain chessboard is being designed so that each square has an area of 3in

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.