SquaresWhat is this shape?

How do you know?

What is the area?

How many small squares areinside the large square?

What is the perimeter?

8181

Perfect Square Activity

What is a Root?

SquaresWhat is a root?

What is the area ofthis square?

What is the root?

Is there any other number Multiplied by itself that equals16?

8181

4

Perfect Squares

• 0 x 0 = 02 = 0• 1 x 1 = 12 = 1 -1 x -1 = (-1)2 = 1• 2 x 2 = 22 = 4 -2 x -2 = (-2)2 = 4• 3 x 3 = 32 = 9 -3 x -3 = (-3)2 = 9• 4 x 4 = 42 = 16 -4 x -4 = (-4)2 = 16• 5 x 5 = 52 = 25 -5 x -5 = (-5)2 = 25• 6 x 6 = 62 = 36 -6 x -6 = (-6)2 = 36• 7 x 7 = 72 = 49 -7 x -7 = (-7)2 = 49• 8 x 8 = 82 = 64 -8 x -8 = (-8)2 = 64• 9 x 9 = 92 = 81 -9 x -9 = (-9)2 = 81• 10 x 10 = 102 = 100 -10 x -10 = (-10)2 = 100

4

16

25

100

144

= 2

= 4

= 5

= 10

= 12

Notes• The root of a square (square root) is equal

to the length of one side of the square• All squares have two roots, one positive

and one negative• Perfect squares have integers for roots• A Radical is the symbol we use to identify

roots• A Radicand is the number or variable

inside the radical 25

Perfect Squares

1

4

916

253649

64

81

100121

144169196

225

256

324

400625

289

361

Estimating Non-Perfect Squares

0 5 101 2 3 4 12119876

• Squares that do not have an integer for a base are called non-perfect squares. For example is a non-perfect square because no integer multiplied by itself equals 20.

• We estimate non-perfect squares by finding which perfect squares they are between:

20

2016 25

16 25

4 55.4

Non-Perfect Squares

Let’s Practice

0 1 2 3 4 5 6 7 8 9 10

Plot:

1. 4.

2. 5.

3. 6.

6

30

55

15

90

75

Perfect Cubes

Perfect Cubes

• How do you find the volume of a cube?

2cm

Perfect Cubes

• How do you find the root of a cube?

8cm3

Perfect Cubes

• What is the volume of this cube?

• What is the root of this cube?

Perfect Cubes

• What is the volume of this cube?

• What is the root of this cube?

Perfect Cubes

• What is the volume of this cube?

• What is the root of this cube?

Let’s Practice

1. 4.

2. 5.

3. 6.

Notes• The root of a cube (cube root) is equal to the

length of one side of the cube

• Perfect cubes have integers for roots

• A small 3 in the hook of the Radical identifies the third, or cube root

• Cubes can have a negative Radicand

Perfect Cubes1 -1

8 -8

27 -27

64 -64

125 -125

216 -216

343 -343

512 -512

729 -729

1000 -1000