Simplifying Radicals Notes
Name ____________________________________
Pd. _________
Objective: To simplify radicals using the multiplication property
Square Roots are made up of 3 parts
x
x
_________________________________
_________________________________
_________________________________
"Roots" (or "radicals") are the ___________________ operation of applying
_____________________; you can ______________ a power with a radical, and a radical
can _____________ a power. For instance, if you “______________ 2”, you get 4 (22 = 4).
And if you "take the _________________________ of 4” (√4 = 2) you get 2.
A perfect square is a number that can be expressed as the product of two equal
integers
Examples of perfect squares
o
_____ is a perfect square because it can be expressed as ____*_____ (the
o
product of two equal integers)
_____ is a perfect square because it can be expressed as ____*_____ (the
product of two equal integers
Non examples of perfect squares
o
8 is a not perfect square because you cannot express it as the product
o
of two equal integers
5 is a not perfect square because it cannot be expressed as the product
of two equal integers
Complete the perfect squares:
12 =
22 =
32 =
42 =
52 =
62 =
72 =
82 =
92 =
102 =
112 =
122 =
132 =
142 =
152 =
162 =
172 =
182 =
192 =
202 =
1=
4=
9=
16 =
25 =
36 =
49 =
64 =
81 =
100 =
121 =
144 =
169 =
196 =
225 =
256 =
289 =
324 =
361 =
400 =
Simplify the radicals:
Simplifying radicals by using the Multiplication Property of Square Roots
Example
Simplify √50
√50 = √25 ∙ 2
25 is a perfect square AND a factor of 50
= √25 ∙ √2
Use Multiplication Property of Square Roots
= 5√2
Simplify √25
Multiplying two Radicals
Example
Simplify the radical expression:
√8 ∙ √12
= √8 ∙ 12
Use the Multiplication Property of Square Roots
= √96
= √16 ∙ 6
16 is a perfect square AND a factor of 96
= √16 ∙ √6 Use the Multiplication Property of square Roots
= 4√6
1.
20 =
2.
18 =
3.
128 =
4.
75 =
5.
12  2 =
6.
10  5 =
Simplify √16
Various Questions with Radicals
3. Estimate the value of 38 to the
nearest whole number.
4. Which pair of consecutive whole
numbers is 52 between?