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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.

## Vocabulary

Terms introduced in this lesson:

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 $\pm$.

Feb 22, 2012

Aug 22, 2014