with square roots. This is an essential skill for working with special right triangle which is an important topic that is
also covered in this chapter. Many students struggle with using roots in algebra, and they have probably not thought
about this topic for a year. Depending on the level of the class, it may be wise to take a day, or half a day, to review
operations with square roots. Here are some sample problems of the basic operations with square roots that student
will have to know how to do in order to be successful in this chapter.
Simplify:
√
9 =
2.
√
50 =
3. 5
√
96 =
Multiply:
√
2 ∗
√
5 =
5. 9
√
6 ∗ 4
√
7 =
6.
√
10 ∗
√
14 =
Square:
7.(
√
7 )^2 =
8.( 3
√
2 )^2 =
Add or Subtract:
√
3 + 7
√
3 =
10. 3
√
5 −
√
20 =
Answers:
- 3
- 5
√
2
3. 20
√
6
4.
√
10
5. 36
√
42
6.
√
140 = 2
√
35
7. 7
8. 9∗ 2 = 18
9. 8
√
3
10. 3
√
5 − 2
√
5 =
√
5
Using Similar Right Triangles
Separate the Three Triangles –The altitude from the right angle of a triangle divides the triangle into two smaller
right triangles that are similar to each other, and to the original triangle. All the relationships among the segments
in this figure are based on the similarity of the three triangles. Many students have trouble rotating shapes in their
minds, or seeing individual polygons when they are overlapping. It is helpful for these students to draw the triangles
separately and oriented in the same direction. After going through the process of turning and redrawing the triangles
a few times, they will remember how the triangles fit together, and this step will no longer be necessary.
2.8. Right Triangle Trigonometry