Unit 9 Review Sheet
Name________________________
Directions: Write each expression in simplest radical form.
3.)
1
72
2
98m9k 8
6.)

11
49
9.)
1.)
112
2.) 3 200
4.)
81x 4 y16
5.)
7.)

3 5

2
8.) 5
32 x12 y 9
2 x4 y3
7
10.) 2
8
11.)
13.) 25 5  14 5  5
14.) 3 12  2 27
12.)
54

2
5
2
81a 3b5
3ab 4
15.) 2 75  108
16.) 7 24  10  2 54  4 90
19.) 6 15  2 10
18.) 5k 3k 2t  27k 4t

21.) 2 5 5 4  80
24.)
27.)
2


2 3 5 4 2 2 5
10  6
2
17.) 25 4 x3  8x 16 x


22.) 3  5 7  5

20.)

25.)
28 90
7 2
28.)
8 2  4 144
4 2
 6

2a5b 5 4ab3

23.) 3  2 6
26.)
29.) Find the length of the side of a rhombus whose diagonals measure 8 m and 12 m.

2
2 54
6 2

30.) The length of a side of a rhombus is 26 cm and the length of one diagonal is 28 cm.
Find, to the nearest tenth, the length of the other diagonal.
31.) The length of a side of an equilateral triangle is 18 centimeters. Find, to the nearest
tenth of a centimeter, the length of the altitude of the triangle.
32.) The length of the altitude to the base of an isosceles triangle is 10 cm and the length of
the base is 14 cm. Find, to the nearest tenth of a cm, the length of each of the legs.
33.) Find the length of the altitude to the bases of isosceles trapezoid KLMN if 𝐾𝐿 = 20 cm,
𝑀𝑁 = 38 cm, and 𝐾𝑁 = 15 cm.
34.) The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments.
If the length of the altitude is 12 and the length of the longer segment is 18, what is the length
of the shorter segment?
35.) If the diagonal of a square has a length of 10, find the perimeter of the square
in simplest radical form.
Directions: In #36 – 41, use the information marked on the picture to find the value of x and/or y.
60◦
36.)
y
x
37.)
38.)
y
x
8
x
39.)
40.)
30◦
y
15
y
C
x
60◦
8
60◦
y
41.)
x
60◦
A 2 D
y
30◦
B
x
Directions: In #42 – 44, the altitude CD is drawn to the hypotenuse AB of right triangle ABC.
42.) If AC  9 and AD  3
find DB .
43.) If AD  5 and DB  8
find CD .
44.) If AD  x , and AB  18
and AC  x  4 ,
find AD and AC .