At the end of this lesson, students will be able to:
- Solve quadratic equations involving perfect squares.
- Approximate solutions of quadratic equations.
- Solve real-world problems using quadratic functions and square roots.
Terms introduced in this lesson:
quadratic equations involving perfect squares
positive, negative square root
Teaching Strategies and Tips
Remind students that:
x2−−√=|x| and is called the principal square root.
|x|=k implies x=±k.
- Conclude that x2=c has two solutions when c>0. See Examples 1-3.
- Point out that square roots of negative numbers are not real numbers. Therefore, x2=c has no solutions when c<0.
Specify in advance the number of decimal places required of students in Examples 6 and 7 and Review Questions 18-22.
In Example 2, show students that 169−−−√=43 and 181−−−√=19. More square-roots of fractions can be found in Review Questions 4-6 and 8.
General Tip: Remind students after square-rooting both sides of an equation to include the ±.