Download Reading Packet: Radical Multiplication Target Goals: 1. Simplify

Algebra II
Name _________________
Reading Packet: Radical Multiplication
Target Goals:
1. Simplify radical expressions
2. Add, subtract, multiply and divide radical expressions
Multiplying Roots
When you multiply roots that have the same index, you multiply the insides of the roots. Then
simplify (aka multiply across and then simplify!)
Example 1:
2
10 x y  40 xy
2
3
10 x y  40 xy
2
OR
3
400
40
10
400 x 3 y 4
400 x 3 y 4
Perfect square route
3
100 * 4 x y
2
Factor Tree route
2  2  2  2  5  5x3 y 4
4
10*2xy 2 x
2  2  5  xy 2 x
20xy2 x
20xy2 x
Example 2: You try (multiply across and simplify)!
12m 2 n  6mn 2
a)
b)
c)
4
4t 3  4 8t 2 u 5
3x 4 z 2  30 x 3 z 9
5
10
4
5
2
2
For example 2, did you get:
a) 6mn 2mn
c) 3x3 z 5 10 xz
b) 2tu 4 2tu
Multiplying Numbers with a number in the front
Rule: When you multiply, you can multiply outside numbers with outside numbers and inside root
numbers with inside root numbers. Then, simplify the roots.
Example 3:
a)
3 2  4 2 multiply the outside numbers and then multiply the roots
3  4 and
2 2
Simplify
12 4
12(2)= 24
What if I added parantheses????

10 2  6
b)



= 10 2  6 DISTRIBUTE (multiply roots together)
= 10  2  10  6
 20  60 **Simplify each root separately
= 4 5  4 15
= 2 5  2 15 No further like terms to combine, so you are done!
Example 4: You try!
a)
2 24  3 4
c)
4 3 27  4 3

b) 23 4  53 4

d)

6 3 5 2

For example 4, did you get:
Example 5:
 mt
3
b) 20 3 2
a) 24 6
c) 84
d) 3 2  10 3
This one is hard! Be careful and take your time on this one!

4 m2  m
3
4  3 16

For example 5, did you get:
m3t
3
4  2m2t
3
2  4mt
FOIL with roots
The Rule: FOIL as we did with binomials, but use the rules that you learned earlier in the packet.
Example 6:

6 3

3 2

Multiply First, Outer, Inner, Last
= 6 3 6 2  3 3 3 2
Simplify by multiplying the roots together
= 18  12  9  6
Simplify by breaking down each radical
= 3 2  2 3 3 6
Example 7: You try!
2
34 5

36 5

For example 7, did you get: 126  16 15
The Conjugate
Foil conjugates. Multiply the following problems as you did above. The conjugate is the special
name when we FOIL 2 parentheses that are the exact same except for the sign in the middle. This
eliminates the middle term.
Example 8:
12  3 12  3 
= 12  12  12  3  12  3  3  3
= 144 -
9
= 144 – 3 = 141
Example 9: You try:
4

5 2 7 4 5 2 7
For example 9, did you get:

52
Example 10: You try: (m  3 4)(m2  m
3
4  3 16)
For example 10, did you get: m3  4
**If you did not get some of the answers listed, go back and try again. If you STILL do not get the
answers, ask a classmate or surrounding group. If you STILL cannot get the answer listed, please
visit the MASH for help tomorrow.