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10.3: Quadratic Equations by Square Roots

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

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
approximate solutions
free fall

Teaching Strategies and Tips

Remind students that:

  • \sqrt{x^2}=|x| and is called the principal square root.
  • |x|=k implies x = \pm k.
  • Conclude that x^2=c has two solutions when c > 0. See Examples 1-3.
  • Point out that square roots of negative numbers are not real numbers. Therefore, x^2=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.

Error Troubleshooting

In Example 2, show students that \sqrt{\frac{16}{9}}=\frac{4}{3} and \sqrt{\frac{1}{81}}=\frac{1}{9}. 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 \pm.

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