Guided Notes: Radicals
SOL A1.3
Name_______________________________________________ Date_______________________
PERFECT SQUARES
A number is a PERFECT SQUARE if ___________________________________________________________
__________________________________________________________________________________________
First 12 Perfect Squares:
NUMBER MULTIPLIED
BY ITSELF
PERFECT
SQUARES
NUMBER MULTIPLIED
BY ITSELF
PERFECT
SQUARES
1X1=
___________
7X7=
___________
2X2=
___________
8X8=
___________
3X3=
___________
9X9=
___________
4X4=
___________
10 X 10 =
___________
5X5=
___________
11 X 11 =
___________
6X6=
___________
12 X 12 =
___________
A variable is a perfect square if it has an _____________ exponent.
VARIABLES MULTIPLIED
BY ITSELF
PERFECT
SQUARES
𝑥∙𝑥 =
___________
𝑥2 ∙ 𝑥2 =
___________
𝑥3 ∙ 𝑥3 =
___________
𝑥4 ∙ 𝑥4 =
___________
SQUARE ROOTS
Taking the square root of a number is the _____________________________________________________
__________________________________________________________________________________________
For example if 32 = _________, then √9 = _________. The symbol √
tells you to ______________________
__________________________________________________________________________________________
Guided Notes: Radicals
SOL A1.3
PARTS OF A RADICAL
An expression that contains a square root is a _____________________. It can have three parts.
Radicand: ________________
Index: _________________________________
_________________________
_____________
______________________________________
Coefficient: _____________________________
Simplify the following radical expressions.
_______________________________________
_
√100 = ___________
√𝑥 4 = ___________
√25 = ___________
√4𝑥 2 =_______________ = _______________
√141 = ___________
√81𝑥 8 𝑦 2 =_______________ = _______________
√𝑥 2 = ___________
√36𝑎6 𝑏 4 =_______________ = _______________
When dealing with exponents, _________________________________________________________ to get
the exponent of the roots.
If your radicand has more than one factor, ____________________________________________________
NON-PERFECT SQUARES
Simplify: √24
Since 24 is not a perfect square, its _____________________________________________. To simplify
this radical, 24 needs to be _______________________________________________________________.
However, one of the factors must be a ________________________.
What is the highest factor of 24 that is also a perfect square? ______. Therefore, 24 = ____ X _____
√24 = √_____ ∙ ______ = √______ ∙ √______ = ____√______
Simplify: √32
What is the highest factor of 32 that is also a perfect square? ______. Therefore, 32 = ____ X _____
√32 = √_____ ∙ ______ = √______ ∙ √______ = ____√______
Guided Notes: Radicals
SOL A1.3
Simplify: √54
What is the highest factor of 54 that is also a perfect square? ______. Therefore, 54 = ____ X _____
√54 =
Simplify: √𝑥 5
What is the highest factor of √𝑥 5 that is also a perfect square? ______. Therefore, 𝑥 5 = ____ X _____
√𝑥 5
= √_____ ∙ ______ = √______ ∙ √______ = ____√______
Simplify: √50𝑥 2 𝑦
What’s the highest factor and perfect square of √50𝑥 2 ? _________. Therefore, 50𝑥 2 = ____ X _____
√50𝑥 2 𝑦 = √_____ ∙ ______ = √______ ∙ √______ = ____√______
Simplify: √42𝑥 9
What is the highest factor and perfect square of √42𝑥 9 ? _______. Therefore 42𝑥 9 = ____ X _____
√42𝑥 9
=
PERFECT CUBES
A number is a PERFECT CUBE if _____________________________________________________________
__________________________________________________________________________________________
First 5 Perfect CUBES and Perfect CUBES Variables
NUMBER MULTIPLIED
BY ITSELF 3 TIMES
PERFECT
CUBES
VARIABLE MULTIPLIED
BY ITSELF 3 TIMES
PERFECT
CUBES
1X1X1=
___________
𝑥∙𝑥∙𝑥 =
___________
2X2X2=
___________
𝑥2 ∙ 𝑥2 ∙ 𝑥2 =
___________
3X3X3=
___________
4X4X4=
___________
___________
𝑥3 ∙ 𝑥3 ∙ 𝑥3 =
A variable is a perfect square if the
exponent is ________________________
5X5X5=
___________
__________________________________
Guided Notes: Radicals
SOL A1.3
Taking the cube root of a number is the _______________________________________________________
__________________________________________________________________________________________
3
3
For example if 23 = _________, then √8 = _________. The symbol √
tells you to ______________________
__________________________________________________________________________________________
Simplify the following radical expressions:
3
√125 = ___________
3
√27 = ___________
3
√𝑥 3 = ___________
3
√64𝑥12 = ___________
NON-PERFECT CUBES
3
Simplify: √54:
What is its highest factor and perfect cube the radicand? ______. Therefore, 54? = ____ X _____
3
3
3
3
√54 = √_____ ∙ ______ = √_____ ∙ √_____ =
3
Simplify: √24𝑥 8 :
What is its highest factor and perfect cube of the radicand? ______. Therefore, 24𝑥 8 ? = ____ X _____
3
3
3
3
3
√24𝑥8 = √_____ ∙ ______ ∙ ______ = √_____ ∙ √_____ ∙ √_____ =