The document provides examples of irrational expressions being added, subtracted, multiplied, divided, and general and particular equations being written. It also contains examples of word problems being solved where variables represent the number of cavities and brushing time. The document demonstrates various arithmetic operations and equations involving irrational expressions as well as solving word problems using proportional reasoning.

1. Irrational (Radical) Expressions

2.  Add
4
28 784

3. 4
28 784
4 7 4
16 4
49
2 7 2 4
7 2
2 7 2 7 4 7
2 7

4.  Subtract
5 10
64 4

5. 5 10
64 4
5 5 10 2
32 2 2
5 2 1
2 2 2 10
2 5
5
5
2 2 5
2 5
2 2

6.  Multiply
3
90 8000

7. 3
90 8000
3 3
9 10 8 1000
3 10 2 10
3 10 20 60 10 20

8.  Divide
3
8 16
3
2

9. 3 3 3
8 16 8 2 8
3 3
2 2
3 3
8 2 8 8 3
8
3
2 1
3 8 2 16
8 8

10.  Write the general equation

11. k
y 3
x

12.  Write the particular equation

13. 9 9
y k x 20 k 512
20 2k k 10
9
y 10 x

14.  Solve the word problem

15. w kV 8 k100
8 8
100
k y x
100
8
24 x 300 x
100

16.  Solve the word problem, again

17. Bob's dentist determined the number of cavities developed in his patient's
mouth each year is inversely proportional to the total number of minutes spent
brushing during each session. If Bob developed four cavities during the year
he spent only 30 seconds brushing his teeth each time, how many annual
cavities will Bob develop if he increases his brushing time to two minutes per
session?
k k
C 4 2 k
m .5
2 2
C ;m minutes C C 1
m 2