Solving Radical Equations
Warm Up
1.
49a8b 2
4. (4 + 6 5) − (9 − 2 5)
2.
3
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3. (80𝑥 ! 𝑦 ! )!
−8y12
!
5.
6. 3 8 + 5 98 − 18
!! !
Examples of Solving Radical Equations
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Fact One: Radical must be alone before you apply the inverse operation. – Before you raise both
sides of an equation to a power, you must isolate the radical.
Fact Two: Always check for extraneous solutions. – Extraneous solution may exist with radical
equations. When we take the square root of a real number, we only want the principal square root
which CANNOT be negative. Therefore, you must check your solutions to determine if extraneous
solutions exist.
1. 2. 2 x + 1 = 14 6 + 3 y − 4 = 9 3. 1
(3x −1) 5 = 2 4. 6. 5. x + 18 = x − 2 Practice Activity
Match each radical equation with its correct solution. Be sure to check for extraneous solutions. When finished, fill in the missing letters to decode the hidden message. Be prepared to present your solution to any of the problems. Work should be shown separately! Solving Radical Equations Homework
Name: __________________
Solve each equation. Check each answer to make sure it is not an extraneous solution.
1. x = 8 1
3
2. ( 6u − 5) + 2 = −3 4
3. 2 x + 6 = 2 4. 4 − x = 3 5. 3x + 7 = x − 1 6. 5x + 1 = 4 x + 3 7. 2 p + 3 = 10 3
8. d + 2 = 7 1
4
9. ( 7 w + 2 ) + 2 = 7 10. 4 3h − 36 = 0 11. Stunt Problem:
The formula s = 21d relates a stunt car driver’s speed s in miles per hour at the beginning of a skid
to the length d of the skid in feet. A stunt driver must skid her car to a stop just in front of a wall. When
the driver starts her skid, she is travelling at 64 mi/hr and is 200 feet from the wall. When the driver
comes to a stop, how many feet will be between her car and the wall? Round to the nearest foot.
12. For a spinning amusement park ride, the velocity v in meters per second of a car moving around a
v = ar , where a is the car’s acceleration in m / s 2
2
For safety reasons, a ride has a minimum acceleration of 39.2 m / s . If the cars on the ride
curve with a radius r meters is given by the formula
a)
have a velocity of 14m/s what is the smallest radius that any curve on the ride may have?
b) What is the acceleration of a car moving at 8m/s around a curve with a radius of 2.5m?