MCR3U
Unit #3 – Class #1
Operations with Radicals I
Textbook: section 3.4 p. 163 – 167 Homework: p. 167 – 168
Definitions:
1. radical

#1, 3, 4, 6, 9, 10,
11, 15 abc, 16,
17
radical sign
5
radicand
2. entire radicals
 examples: 7 , 101
 there is no real number in front of the radical sign
3. mixed radicals
 the radical is a product of a real number and a radicand
1
17
 examples: 2 5 ,
17 
2
2
 2 5  2 5
4. like radicals
 radicals that have the same radicand
2
2 3
 examples: 3 , 2 3 ,  4 3 ,
3
3
3
5. unlike radicals
 radicals that do not have the same radicand
 examples: 2 5 , 5 2 ,  7 3 , 4 7
6. simplifying radicals
 means to express the radical with the smallest possible radicand
 the radicand has no factors that are perfect squares because the
largest possible perfect square factor has been pulled out
7. adding and subtracting radicals
 only like radicals can be combined
 similar to adding and subtracting like terms
 must simplify each individual radical first
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MCR3U
Examples:
Unit #3 – Class #1
Simplify.
a)
98  49  2
 49  2
7 2
b)
300  100  3
 10 3
c)
4 54  4 9  6
 
43 6
 12 6
d)
1
1
28 
4 7
2
2
1
 2 7
2
 7
 
e) 4 3  6 3  2 3
f) 9 5  6 7  9 7  11 5  20 5  15 7
g)
27  12  3 3  2 3
 3
h)
18  75  3 200 

  
1
1
48  3 2  5 3  3 10 2  4 3
2
2
 3 2  5 3  30 2  2 3
 27 2  7 3
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