Squares, Cubes and Roots

8th Grade Math 2013-14

MCC8EE2, MCC8NS1, MCC8NS2

POD 17 Sep Evaluate1. –122

2. (a4b3)(a5b2)

Simplify; write solution in Scientific Notation:

3. 3 x 10-3 • 4 x 104

4. .00065 x 103

POD 18 SepUse the information given to find the measures of:1. angle d

l1 || l2 and l3 || l4

l1

l2

l3 l4

ab

c

de

fg

h

j ki

540

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?

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?• The length of 1 side of a square is the

square root, and the length of 1 side of a cube is the cube root

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

Compare Numbers• Compare the following numbers by placing

<, >, <, >, or = in the box.

1. 5

2. 8.5

3.