Squares & Roots
Square a Number
Multiply a number by itself to square it.
Make a square 2 high x 2 wide = area 4.
2 squared = 2 × 2 = 4
2 = 4
2
A square is a closed figure with 4 equal straight sides and only right angles.
Squares
1×1 = 1
1
1|1
2×2 = 4
2
2|4
3×3 = 9
3
3|9
4×4 = 16
4
4|16
7×7 = 49
7
7|49
5×5 = 25
5
5|25
6×6 = 36
6
6|36
8×8 = 64
8
8|64
9×9 = 81
9
9|81
10×10 = 100
10
10|100
A square is a rectangle with 4 equal sides and 4 right angles.
Vertical side x horizontal side = area
The area of the square is the product of two same factors.
"4 squared " is 16 because
a 4 by 4 square
is 4 units high and 4 units wide
and contains 16 units inside
the area of the square.
4×4 = 16
4 wide
4 high|16 area
4×4 = 16
quotient
divisor|dividend
100
81
64
49
36
25
16
9
4
16
2
2
2 high x 2 wide
= Area of 4 unit squares
A PERFECT SQUARE is a RECTANGLE with all sides the same size.
The number of unit squares INSIDE the square is its AREA.
The ROOT of a SQUARE is the length of it's bottom.
The size of its bottom is the same as its other sides!
What is the ◾SQUARE ROOT of 4?
What is the ROOT or what would CAUSE
a SQUARE to have an AREA of 4?
Having a side of 2 would cause a square to have an area of 4 because
2 units high by 2 units across
results in 4 units inside the square.
The square root of 4 is 2.
The area of 4 has a
root of 2.
Get to the bottom of it!
Find the root of the problem!
What causes a square to have an area of 4?
A root or side measuring 2 makes a square with an area of 4.
4
The radical symbol can be used instead of the words, "square root."
√4 means, "What is the square root of 4?"
The area number goes inside the square of the radical symbol.
√4 = 2
2
Square a Number
2 squared = 4
2 × 2 = 4
2 = 4
√4 = 2
2|4
√ =
because
2 units wide
2 times
makes a square with
4 units inside,
where the area is 4.
2
2
2
2
2
Squares and Square Roots Many Ways
Three squared means, "What's the area of a square with a side of 3?"
3 squared means, "What's the area of a 3 by 3 square?"
3 means 3 × 3 = 9 area
2
3×3 = 9
3|9
3
3
2
= 3 × 3 = 9
1
2
Square Root 13 Ways
What is the square root of nine?
√9
√9
9
If a square has an area of 9, what is the length of its side?
What is the root of a square with an area of 9?
If a square has an area of 9, how high is it?
What is the height of a square with an area of 9?
If a square has an area of 9, what is its width?
How wide is a square with an area of 9?
What number multiplied by itself is 9?
What number squared is 9?
A square contains nine units. What is the length of its side?
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2
2
2
2
2
2
2
2
2
2
2
2
2
1 × 1 = 1 1 = 1 one squared = 1 √1 = 1 1 = 1
2
2
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2
1
__
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2
_
1
2
2
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1
2
_
■ root
■ root
The ■ root of 1 is 1.
2 × 2 = 4 2 = 4 two squared = 4 √4 = 2 4 = 2
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The ■ root of 4 is 2.
■ root
■ root
3 × 3 = 9 3 = 9 three squared = 9 √9 = 3 9 = 3
The ■ root of 9 is 3.
■ root
■ root
4 × 4 = 16 4 = 16 4 squared = 16 √16 = 4 16 = 4
_
1
2
1
The ■ root of 16 is 4..
■ root
■ root
5 × 5 = 25 5 = 25 5 squared = 25 √25 = 5 25 = 5
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The ■ root of 25 is 5..
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_
2
7 × 7 = 49 7 = 49 7 squared = 49 √49 = 7 49 = 7
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The ■ root of 49 is 7..
■ root
■ root
■ root
■ root
1
1
6 × 6 = 36 6 = 36 6 squared = 36 √36 = 6 36 = 6
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1
2
_
_
The ■ root of 36 is 6..
■ root
■ root
8 × 8 = 64 8 = 64 8 squared = 64 √64 = 8 64 = 8
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2
The ■ root of 64 is 8.
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1
2
■ root
■ root
9 × 9 = 81 9 = 81 9 squared = 81 √81 = 9 81 = 9
__
_
1
2
The ■ root of 81 is 9.
■ root
■ root
10 × 10 = 100 10 = 100 10 squared = 100 √100 = 10 100 = 10
The ■ root of 100 is 10..
1
1
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2
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11 × 11 = 121 11 = 121 11 squared = 121 √121 = 11 121 = 11
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2
2
■ root
■ root
The ■ root of 121 is 11..
■ root
■ root
12 × 12 = 144 12 = 144 12 squared = 144 √144 = 12 144 = 12
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The ■ root of 144 is 12..
■ root
■ root
13 × 13 = 169 13 = 169 13 squared = 169 √169 = 13 169 = 13
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The ■ root of 169 is 13..
■ root
■ root
14 × 14 = 196 14 = 196 14 squared = 196 √196 = 14 196 = 14
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1
_
2
The ■ root of 196 is 10..
■ root
■ root
_
2
1
1
_
15 × 15 = 225 15 = 225 15 squared = 225 √225 = 15 225 = 15
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_
2
The ■ root of 225 is 15..
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16 × 16 = 256 16 = 256 16 squared = 256 √256 = 16 256 = 16
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2
1
1
■ root
■ root
The ■ root of 256 is 16..
■ root
■ root
2
17 × 17 = 289 17 = 289 17 squared = 289 √289 = 17 289 = 17
2
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1
2
18 × 18 = 324 18 = 324 18 squared = 324 √324 = 18 324 = 18
2
_
1
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19 × 19 = 361 19 = 361 19 squared = 361 √361 = 19 361 = 19
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1
_
2
The ■ root of 289 is 17..
The ■ root of 324 is 18.
The ■ root of 361 is 19..
The ■ root of 400 is 20..
■ root
■ root
■ root
■ root
■ root
■ root
20 × 20 = 400 20 = 400 20 squared = 400 √400 = 20 400 = 20
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■ root
■ root
2
2
