Solve Equations with Square Roots

Lesson 15 Solving Square Root Equations

TEKS 2A.3D, 4F, 4G, 7H

We will solve square root equations algebraically and graphically.
I will summarize the process of solving square root equations and finding extraneous solutions.

Solving a Radical Equation

Let's look at two examples:

Open Ended

After viewing the algebraic methods of solving these equations, how might you use technology to find solutions?

Let's talk about Extraneous Solutions before graphing...

Let's try solving equations graphically

Multiple Choice

Solve: $$\sqrt[]{x}=\frac{1}{9}$$

•  $$\frac{1}{18}$$

• 0
• $$\frac{1}{81}$$

•  $$\frac{1}{36}$$

Multiple Choice

Solve: $$\frac{2}{5}\sqrt[]{10x+6}=12$$

• 89.4
• 75.1
• 50.2
• 24.5

Multiple Choice

Solve: $$\sqrt[]{x^2+5}=x+3$$

• $$-\frac{5}{3}$$

• 3
• $$-\frac{2}{3}$$

•  $$\frac{1}{2}$$

Math Response

In a right circular cone with a slant height of 1 unit, the radius r of a cone is given by $$r=\frac{1}{\sqrt[]{\pi}}\sqrt[]{S+\frac{\pi}{4}}-\frac{1}{2}$$ , where S is the surface area of the cone. Graph the model. Then find the surface area of a right circular cone with a slant height of 1 unit and a radius of 1/2 unit. Keep your answer in terms of pi.

Type answer here

Correct Answer: \frac{3\pi}{4}

Deg^°

Rad