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Algebra II – Chapter 6 Day #2
Topic: Adding, Subtracting, Multiplying & Dividing Radical Expressions
Standards/Goals:
 A.SSE.2: I can take the structure of an expression and identify different ways to
rewrite it
 G.1.d.: I can add, subtract, multiply, and divide expressions containing radicals.
 G.1.b.: I can simplify radicals that have various indices.
FLASHBACK Review:
Simplify each radical expression.
𝟒
#1. √𝟑𝟔𝒙𝟒
#2. √𝒄𝟖𝟎 𝒅𝟓𝟎
#3. √𝟖𝟏𝒙𝟏𝟐
#4. √𝟐𝟓𝒙𝟔 𝒚𝟕
𝟓
𝟑
#6. √−𝟑𝟐𝒌𝟓
#5. √−𝟔𝟒
We first want to focus on how to MULTIPLY radical expressions.
Let’s first look at some important properties for combining radical expressions using
multiplication.
𝑛
𝑛
If √𝑎 and √𝑏 are real numbers, then:
EXAMPLES:
Can you simplify the following products? If so, then do it.
4
4
4
4
#1. √64 ∗ √32
#2. √125 ∗ √405
Simplify the following expressions.
3
#1. √54𝑥 5
3
#3. √135𝑥 5
3
#3. √6 ∗ √2
4
#2. √162𝑥 6
#4. √54𝑥 4 𝑦 3 ∗ √72𝑥𝑦 6
2
We next want to focus on how to DIVIDE radical expressions.
Let’s first look at an important property for combining radical expressions using division.
𝑛
𝑛
If √𝑎 and √𝑏 are real numbers and b ≠ 0, then:
EXAMPLES:
Simplify the following expressions.
√18𝑥 5
#1.
√2𝑥 3
#2.
3
√64𝑥 7
#3.
√4𝑥 3
√189𝑥 7
3
√7𝑥 2
We next want to learn how to add and subtract radicals.
It’s very important that approach adding and subtracting radical expressions thinking in
terms of LIKE TERMS.
Examples:
3
3
#1. 2𝑥 4 + 3𝑥 4 − 6𝑥 2
#2. 2√6𝑥 + 3√6𝑥 + √6𝑥
Let’s take some time to look at a property pertaining to finding the sum and difference of
radical expressions.
Use the Distributive Property to add or subtract like radicals:
EXAMPLES:
What is the simplified form of each expression?
5
5
#1. 14𝑎√7𝑏𝑐 + 5𝑎√7𝑏𝑐
#2. 3 √𝑥 − √3𝑥
4
4
4
#3. 15 √8𝑦 3 − 6 √8𝑦 3 + √𝑦 3
3
Sometimes, we have to simplify what is under the radical before we can add or subtract.
EXAMPLES: Simplify each:
#1. 2√7 + 3√7
#2. √32 + √8
#3. √7𝑥 + √28𝑥
#4. 3√18 + 2√72
#5. √27 + √48
#6. 8√45 − 3√80
#7. √180 − √80 + √45
#8. √28 − √175 + √63
#9. √12 + √75 − √3
#10. √250 + √54 − √16
3
3
3
4
HOMEWORK – Chapter 6 Day #2
Name ________________________________________ Date _______
Multiply, if possible. Then simplify. To start, identify the index of each radical.
43 6
3
1.
2.
64 9
3
5 8
3.
Simplify. Assume all variables are positive. To start, find all perfect square factors.
3
27x 6
4.
5.
48x3 y 4
5
6.

5  15
Multiply/Divide and simplify. Assume all variables are positive.
4
7.
12  3
4
8.
7 x 6  4 32 x 2
9.
√36𝑥 6
√9𝑥 4
405 x8 y 2
4
10.
5 x3 y 2
Simplify: Add or subtract if possible.
11.
9 32 3
12. 14
13.
5 3 xy  3 xy
14.
15.
3 32  2 50
16.
200  72
17.
81  3 3 3
18.
3 75  2 12
19.
28  63
20.
125  2 20
3
3
xy  3 3 xy
3x  2 3x
