Perfect Squares & Square Roots
Integrated Mathematics
Perfect Squares
 The Squares of Whole Numbers
 Whole Number Multiplied by Itself
12 = 1
62 = 36
22 = 4
72 = 49
32 = 9
42 = 16
52 = 25
82 = 64
112 = 121
122 = 144
132 = 169
162 = 256
172 = 289
182 = 324
92 = 81
142 = 196
192 = 361
102 = 100
152 = 225
202 = 400
 No Fractions or Decimals
2
0.5
12
2
Square Roots
 The square root of a number can be multiplied by
itself, or squared, to equal the number
Examples
Ex.1) 𝟏𝟎𝟎
Ex.2) 𝟐𝟓
Ex.3) 𝟒𝟗
 Every positive number has 2 square roots that are
opposite in sign
Simplify the Square Roots
 Find a perfect square that multiplies with another
whole number to equal the number under the radical
 Simplify the perfect square
Ex.4) 𝟒𝟓
Ex.5) 𝟕𝟐
Simplify the Square Roots
 Find a perfect square that multiplies with another
whole number to equal the number under the radical
 Simplify the perfect square
Ex.6) 𝟏𝟐𝒙𝟐
Ex.7) 𝟑𝟐𝒙𝟒
Simplify the Square Roots
 Find a perfect square that multiplies with another
whole number to equal the number under the radical
 Simplify the perfect square
Ex.8) 𝟗𝟖𝒙𝟕
Estimating Square Roots
 Determine 2 Perfect Squares in which the number
under the radical fall in between
Ex.9) 𝟑𝟓
Ex.10) 𝟔
Estimating Square Roots
 Determine 2 Perfect Squares in which the number
under the radical fall in between
Ex.11) 𝟕𝟏
Ex.12) 𝟐𝟑
Estimating Square Roots
Ex.13) 𝟑𝟕
Ex.14) 𝟗𝟕
Estimating Square Roots
Ex.15) 𝟏𝟕