5.1 Part 1 Simplifying Radicals
PC 11
Name_______________________________ Date: _________________________
Block_____
1. Simplify
a. 3 25
16
9
b.
c.
3
3
d. 5 27
8
e.
4
2. Write in simplest radical form.
a.
e.
8
2
72
3
b.
f.
3
45
c. 112
d.
54
g. 5 3 27
h. 74 80
10 12
3. Write each expression in simplest radical form.
a.
25 x 2
b.
e.
24x 7 y
f.
x7
c.
4x
9 y2
g.
3
c.
2
5
3
xy 5
d.
8x 4 y 2
h.
3
x3
25 96x 5 y 6
4. Write as an entire radical.
a. 2 5
b. 3 7
e. 4 3 7
f.
23
7
5
d. 23 3
g. 24 3
h. 2 5 3
5. Write as an entire radical.
a. x y
b. xy x
e. x 2 3 x
f. 2x
4
y
2
c. 2xy x
g.
1
3x
2x
d. 3x 5 xy
3
h.
2x
y2
6. Order each set of numbers from least to greatest.
a. 24, 3 2 , 2 5
b. 2 5 , 3 7 ,
3 2, 5 3
81
7. Identify the restrictions on the variables.
a. 3 2a
b.
3z 2
e)
x 9
c.
f. 3 y 2
3
g.
x 12
d.
8y
h. Simplify first , then
determine the restriction.
5z 3
2 x5y2
8a. A square has an area of 48 cm2. Determine the side length of the square.
b.
Determine the length of the diagonal of the square.
9. A cube as a volume of 128 cm3. What is the length of each side?
Answers:
1a. 15 b.
4
c. 2 d. 15 e. -3
3
3a. 5x b. x
3
20 b.
63 c.
5a.
x 2 y b.
x 3 y 2 c.
7e.
3 2 , 2 5 , 24
z
2 2 b. 3 5
x c. y 2 xy d. x e. 2 x 3 6xy
4a.
6a.
2a.
b.
20
9
d.
3
24
4 x 3 y 4 d.
2 5,
e.
3
c. 4 7
f.
2
x g. 2 x 3 xy 2
3y
448 f.
9 x11 y e.
3
3
56
125
x 7 f.
3 2 , 3 7 , 5 3 7a. a
2
f. no restrictions g. no restrictions h. x
3
20 3 e. 4 2 f. 33 2 g. 15 h. 14 4 5
d.
0
g.
4
0
4
48 h.
x
9
5
96
3
h
4x
16x 4 y g.
b.
4 xy 5 3 y
h.
c.
3
x 12
8a. 4 3 cm b. 4 6
9.
2x
y6
d. z
43 2
3
5