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Radicals
Ms. Cardenas
Homework 2
Due date: 01/20/2023
SWBAT add and
subtract, multiply and
divide different forms
of radical numbers IOT
solve and simplify
radical expressions.
OBJECTIVE
What is a radical?
• "Roots" (or "radicals") are the "opposite" operation
of applying exponents;
If there is no index, it is assumed that 𝑛 = 2
…
We can "undo" a power with a radical, and we can
"undo" a radical with a power.
22 = 4, 4 = 2
32 = 9, 9 = 3
VIDEO TIME
• https://www.youtube.com/watch?v=B-Sfvry_h3Q
8
What numbers are perfect squares?
1•1=1
2•2=4
3•3=9
4 • 4 = 16
5 • 5 = 25
6 • 6 = 36
49, 64, 81, 100, 121, 144, ...
Perfect Squares
1
64
225
4
81
256
9
16
100
121
289
25
36
49
144
169
196
400
324
625
4
=2
16
=4
25
=5
100
= 10
144
= 12
Simplifying Radicals
1. Find the largest perfect square that the radicand is
divisible by.
Break down the radical using this number.
2. Take the square root of the perfect square. Take it out of
the radical.
3. Leave the “leftover” under the radical symbol.
12
LEAVE IN RADICAL FORM
Perfect Square Factor * Other Factor
8
=
4*2 =
2 2
20
=
4*5
=
2 5
32
=
16 * 2 =
4 2
75
=
25 * 3 =
5 3
40
=
4 *10 = 2 10
Simplify radicals by removing perfect-square
factors.
Example 1
50 =
Example 2
28 =
14
Simplify radicals by removing perfect-square
factors.
Example 3
18 =
Example 4
250 =
15
PRACTICE
• Delta MATH  Simplifying radicals
• Individual work
• Work silently
• CELL PHONE IS NOT ALLOWED!
16
Remove your
earbuds and put
the cellphone inside
your backpack
17
Examples
• 96 =
• 3 20 =
• 60 =
• 2 64 =
Teamwork
• Worksheet  Simplifying radicals
• Teamwork (2 members per team)
• Work silently
• CELL PHONE IS NOT ALLOWED!
As soon as you
finish your
teamwork, start
solving your
homework.
This is not a time to
use the cellphone.
19
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Examples
• 36 =
• 2 60 =
• 50 =
• 120 =
https://www.youtube.com/watch?v=YBgi93bqk6g
YOUR TURN! 
Get a whiteboard
and a marker
• Simplify:
22
Add and subtract radicals
 To add or subtract radicals you must have like radicals.
 Like radicals must have the same index and same radicand.
 3 5 and 2 5 are like radicals.
3
 6 3 and −4 3 are NOT like radicals.
 7 6 and 2 5 are NOT like radicals.
 For the radicals, just as with like terms, you add or subtract
the coefficient & keep the radicand.
 If necessary, simplify radicals before adding or subtracting by
taking out the perfect square.
23
Simplifying radical expressions
• 2 5+3 5=
• 3 13 − 4 13 =
•6 7 − 7=
• 3 10 − 2 10 + 6 10 =
• −9 6 − 6 6 =
• 17 3 − 2 3 − 15 3 =
24
YOUR TURN! 
Get a whiteboard
and a marker
• Simplify:
25
PRACTICE
• Worksheet  Adding and subtracting radicals
• Individual work
• Work silently
• CELL PHONE IS NOT ALLOWED!
26
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Examples
• 3 + 12 =
• 75 − 25 =
• 8 + 18 =
• 3 5−5 3=
28
Examples
• − 3 + 6 27 =
• −3 7 − 7 28 =
• 96 − 32 − 24 =
• 20 + 40 + 60 =
29
Assignment
• MATH XL  Adding and
subtracting radicals
• Induvial work
• Work silently
• CELL PHONE IS NOT ALLOWED!
As soon as you
finish your work,
continue with your
homework.
This is not a time to
use the cellphone.
30
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31
Examples
• 3 6 − 96 =
• −8 27 − 3 27 =
• −9 108 + 27 =
32
Assignment
• MATH XL  Adding and
subtracting radicals 2
• Induvial work
• Work silently
• CELL PHONE IS NOT ALLOWED!
As soon as you
finish your work,
continue with your
homework.
This is not a time to
use the cellphone.
33
Remove your
earbuds and put
the cellphone inside
your backpack
34
VIDEO
https://www.youtube.com/watch?v=EzjfPAeMU
d0
35
Multiply and divide radicals
 To multiply radical expressions, you multiply the
coefficients, and the radicals then simplify.
 Follow exponents rules (add when multiplying exponents
with the same base).
 To divide radical expressions, you can simplify before
breaking down the radicand if possible or break it down
then simplify.
 Follow exponents rules (subtract when dividing exponents
with the same base).
36
Multiply and divide radicals
 If numerator has a radical and denominator does not, you
must simplify the radical before dividing.
 You can not have a radical in the denominator so you must
rationalize by multiplying by the denominator to clear it.
37
Examples
• 7 × 28 =
• 2 × 18 =
• 2 3×3 8=
• 3( 18 − 3) =
38
Examples
•
240
4
•
20
4
=
=
•
6
7
=
•
5
7
=
39
PRACTICE
• Worksheet  Multiplying and dividing radicals
• Individual work
• Work silently
• CELL PHONE IS NOT ALLOWED!
40
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DFA REVIEW
• Question 1
Simplify the radical expression.
175
42
DFA REVIEW
• Question 2
Simplify the product.
3 × 48 =
43
DFA REVIEW
• Question 3
Simplify the difference.
10 3 − 27 =
44
DFA REVIEW
• Question 4
Simplify the radical expression.
150
3
=
45
DFA REVIEW
• Question 5
Simplify the radical expression.
6 27 + 48 − 18 =
46
DFA
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DFA3-2A-Radicals.
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RETAKE - DFA
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Access to MATH XL 
DFA3-2B-Radicals.
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48