MPM 1DE
U2-7 Simplifying Radical Expressions Homework Sheet
1. Simplify. Leave answer exact (radical form) and in simplest form.
a) 2 2  2 3  4 2
b) 3 2  2 3  4 2  5 3
c) 5 5  2 7  2 7  3 3  4 3
d) 2 2  6 8
e)
48  3 3
f) 2 6  4 24
g)  3 75  2 27
h)
8  12  18  27
i) 2 20  3 45  80
j)  48  50  2 18  75 k) 2 45  3 27  20  48
l)
4 50 2 27
2 18

 3 48 
5
3
3
2. Simplify. Express your answer in simplest radical form.
a) 3 2  5 6
b) (  10 )( 2 )
e) ( 6 8 )(3 27 )
f)

i)  2 50

2
48  2 108
j)  3( 4 3  2)  2(8  2 3 )
c)
20  12
g) 2 10  3 100
d) 2 64  3 100
h) (3 3 ) 2
k) 2( 3  3 2 )  3(6 3  2 2 )
3. Simplify. Express your answer in simplest radical form.
a)
9 18
3
b)
15 75
3 25
c)
 24
8
4.A spiral is formed with right triangles, as shown in the diagram.
a) Calculate the length of the hypotenuse of each triangle, leaving your answers in radical form. Describe the pattern that
results.
b) Calculate the area of the spiral shown.
c) Describe how the expression for the area would change if the pattern continued.
d) Extend the spiral as far as you can without overlapping.
ANSWERS
1. a) 6 2  2 3
b) 7 2  3 3
c) 5 5  3
d)  10 2
g)  21 3
h) 5 2  5 3
i)  5
j)
b) 2 5
c) 4 15
d) 480
e) 108 6
g) 60 10
h) 27
i) 200
j) 22  8 3
b) 5 3
c)  3
3 2
e)
3 f)  6 6
k) 8 5  13 3
l) 2 2  10 3
2. a) 30 3
f) 144
k)  16 3
3. a) 9 6
4. a) a 
2 , b  3 , c  4  2, d  5
b) A 

1
1 2  3 4
2

c) The area of the spiral will be one half the sum of the square root of one to the number of triangles.
d)