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?