P R A C T I C E
Simplify each radical expression
3
3
√8
3√54
4 ± √40
Unit 7 Lesson 1
√75𝑥 2
√28𝑥 4 𝑦 5
3
√54𝑥 3 𝑦 3
Simplifying √𝑹𝑨𝑫𝑰𝑪𝑨𝑳 Expressions
Objectives: SWBAT (1)simplify radical expressions using
prime factorization (2) solve radical equations
Why tho? We are prepping for solving quadratic equations,
which means we need to know how to simplify radicals
V O C A B U L A R Y
−2 ± √64
5
3 − √60
7
Challenge:
4
√96
Warm Up: Prime Factorization Practice
Write the prime factorization for each
number
Index - tells you what size of IDENTICAL
groups of numbers or variables can be
removed from the radicand
If the index is not written, it automatically is a

______.
Prime Factorization – finding which numbers multiply
together to make the original number
Useful Resource: Prime Numbers 1-53
Prime Numbers – numbers that only
have factors of _____ and itself
Why does prime factorization work?
The inverse operation of squares roots, cube roots, nth
roots, is to raise it to the nth power.
 an nth roots and radical “cancel” each other out
Example:
3
3
( √8) = 8
2
(√25) = 25
30 =______________
81 =___________
Directions: Write the radical expression in simplest form
Square Roots of Perfect
EXAMPLES
√75
Squares
3 √28𝑥 3
√1 = _________
√4 = _________
√9 = _________
√16 = _________
2 + √99
2 + √36
3
√25 = _________
√36 = _________
56 =_____________
72 =____________
√49 = _________
3
4√81
√64 = _________
S I M P L I F Y I N G √𝒓𝒂𝒅𝒊𝒄𝒂𝒍𝒔 STEPS
UNO: Find the prime factorization
√81 = _________
√100 = _________
TWO: Pull out identical groups based on the index (circle
each group)
√58
TRES: For each circled group, the number or variable is
multiplied by the coefficient of the radial
If everything is removed from the radicand, the radical
symbol will disappear
Simplifying Radical Expressions
EXAMPLE + PRACTICE
Y O U TRY
2√49 + 3
−2 + √49
3