1. 6.4 – nth Roots

2. Inverse Operations:
The inverse of raising a number to the nth power is finding the nth root of a number.

3. nth Root:

5. nth roots in calculator

6. Example 1:
Simplify

7. Example 2:
Simplify

8. Example 3:
Simplify

9. Example 4:
Simplify

10. Example 5:
Simplify

11. Example 6:
Simplify

12. Example 7:
Designers must create satellites that can resist damage from being struck by small particles of dust and rocks. A study showed that the diameter in millimeters d of the hole created in a solar cell by a dust particle traveling with energy k in joules is about
a. Estimate the diameter of a hole created by a particle traveling with energy 3.5 joules.
b. If a hole has diameter of 2.5 millimeters, estimate the energy with which the particle that made the hole was traveling.

13. Example 8:
The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula
where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared.
Find the value of T for a 2-foot-long pendulum.
b. How long is the pendulum if it takes 5 seconds to swing back and forth?

14. Ticket Out:
Simplify