1. Radical Equations and Problem Solving
Section
10.6
Radical Equations and Problem Solving

2. Solving a Radical Equation
Step 1: Isolate one radical on one side of the equation.
Step 2: Raise each side of the equation to a power equal to the index of the radical and simplify.
Step 3: If equation still contains a radical, repeat steps 1 and 2. If not, solve equation.
Step 4: Check proposed solutions in the original equation.

3. Example
Solve.

4. Example
Solve:

5. Example
Solve:
continued

6. Example
Solve:
continued

7. Example
Solve:

8. Example Solve. Substitute into the original equation.
Does NOT check, since the left side of the equation is asking for the principal square root.
So the solution is .

9. The Pythagorean Theorem
If a and b are lengths of the legs of a right triangle and c is the length of the hypotenuse, then
a2 + b2 = c2.

10. Example
Find the length of the hypotenuse of a right triangle when the length of the two legs are 2 inches and 7 inches.

11. Example
Find the length of the leg of a right triangle. Give the exact length and a two-decimal-approximation. Let a = 2 meters and c = 9 meters.

12. Example
A surveyor must determine the distance across a lake at points P and Q as shown in the figure. To do this, she finds a third point, R, perpendicular to line PQ. If the length of PQ is 320 feet and the length of QR is 240 feet, what is the distance across the lake? Approximate the distance to the nearest whole foot.
Continued 12