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Multiplying and Dividing Square Roots:
Example:
a)
c)
d)
If two square roots are being multiplied or divided,
then write a single square roots and move the
multiplication or division inside that square root.
Perform the following operations and simplify all radicals:
 2  3 
23 
3 5 4 10   34
6
510  12
b)
24

8
24
 3
8
  2   125 2 
50  12 25
  2   163 2   48
 32  54 
  
 16 18  16 9
2 3
 2  3 
32 54
2
NOW DO EXERCISE 2 ON THE WORKSHEET!
Like Square Roots: Like Square Roots are square roots that have the same number inside the
radical sign.
Examples:
Like Square Roots:
3,
4 3,
2 3
NOT Like Square Roots:
3,
4 5,
2 7
Adding and Subtracting Square Roots:
ONLY like square roots can be added or
subtracted...carry the common square root and add
or subtract the coefficients (numbers in front of the
square root).
Examples:
Perform the following operations and simplify the radicals:
a) 3 5  7 5  8 5  4 5
----------------------------------------------------------------------------------------------------------------b)
50  18
NOTE: These are not like square roots and can’t be added but they can be
simplified.

 25  2    9  2   5
2 3 2
Once they are simplified we notice that they are now like square roots and can now be added.
=8
2
----------------------------------------------------------------------------------------------------------------------------- ----------
  7    9  7 
 32 7   3 7 

3 28  63  3 4
c)
6 7 3 7 3 7
d)
2 3

3 2

 6 4 9 6
 2 6  2  3  2 6 1
NOW DO EXCERCISES 1,2 and 3 ON THE WORKSHEET!
Square Roots and Operations with Radicals
Worksheet
1. Perform the following operations and simplify all radicals:
a)
d)
 2  5 
72
b)
e)
6
3 2  6 
50
c)
f)
5
g)
 8 
h)
j)
 2  9  10 




 5  2  3 




k)
1


2


2 15 3 30 
7
 8  6 
27 490
9 5
i)
l)
63
6 2 6 18 
24 56
6 7
2. Perform the following operations and simplify all radicals:
a)
3 54 5
b)
2 7 7 2
c)
14 8  5 8
d)
2 11  7 11  4 11
e)
7 6 4 3 3 6 2 2
f)
8  18
75  20
g)
j)
h)
3 72  2 75  3 27  108
27  48  2 3
k)
i)
 5 44  2 99
250  135  40  735
3. Perform the following operations and simplify radicals:
a)

c)
2
e)

5 3

5 2
8 6

5 3

2

3 6

b)

6 2

d)

2 6
2
 10  3 