1. Multiplying & Dividing Radical Expressions

2. Gm1m2 r2
The formula F =
relates the gravitational force F between an object of mass m1 and an object of mass m2 separated by a distance r. G is a constant known as the constant of gravitation. Solve the formula for r.
To accomplish this, we need to know how to multiply and divide with radicals.

3. Property:
In other words, a radical times another radical is a bigger radical.

4. Examples:
Simplify if possible.

5. The radicals must have the same index to do this.
Examples:
The radicals must have the same index to do this.
Simplify if possible.

6. Examples:
We cannot multiply these at the moment…they do not have the same index.

7. Examples:
The property for multiplying radicals does not apply here since -4 is not a real number.

8. Group Numbers and like variables.
Simplifying Radical Expressions:
Now split apart the variables into powers that are multiples of the index.
Simplify the numbers.
Group Numbers and like variables.

9. Simplifying Radical Expressions:

10. Simplifying Radical Expressions:

11. Your Turn: = = =  =

12. Property:
In other words, a radical divided by another radical is a smaller radical.

13. The radicals must have the same index to do this.
Examples:
The radicals must have the same index to do this. =

14. Examples: = = = = = =

15. Your Turn: = = =

16. Basic Rules of Radicals:
You can’t leave a perfect nth power factor under the radical.
You can’t leave a fraction under a radical (this includes decimals).
You can’t leave a radical in the denominator of a fraction.

17. You must RATIONALIZE denominators.
We call clearing a denominator of radicals RATIONALIZATION.
You must RATIONALIZE denominators.
RATIONALIZE by turning the denominator into a perfect power.

18. Place the expressions under one radical.
Examples: = = =
Simplify.
Place the expressions under one radical.

19. = = =  = = Examples: Place the expressions under one radical.
You can’t leave a fraction under the radical.
Simplify.
Rationalize…Turn the denominator into a perfect square. =

20. Examples: = = = =  = = =

21. Examples: = = = =  = = =

22. Examples: = = = = = =

23.  = = =

24. The volume of a sphere of radius r is:
Use the formula to find r in terms of V. Rationalize the denominator.
Use your answer above to find the radius of a sphere with volume 100 in3. Round to the nearest hundredth.