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Skill 7 Solutions - Square Numbers vs. Square Roots
1) List all of the “square numbers” or “perfect squares” from 1 to 200.
1 i 1 = 1 , 2 i 2 = 4 , 3 i 3 = 9 , 4 i 4 = 16 , 5 i 5 = 25 , 6 i 6 = 36 ,
7 i 7 = 49 , 8 i 8 = 64 , 9 i 9 = 81 , 10 i 10 = 100 , 11 i 11 = 121 ,
12 i 12 = 144 , 13 i 13 = 169 , 14 i 14 = 196
2) List all factor pairs of the numbers below, without repeating factors (excluding 1). Then rewrite any “square
number” as a number squared.
b) 48
d) 50
a) 24
c) 54
Factors
Factors
Factors
Factors
2 • 12
3•8
4•6
2 • 24
3 • 16
4 • 12 2 • 27
3 • 18
6•9
2 • 25
5 • 10
6•8
Factors as Squares
(2)2 • 6
Factors as Squares
3 • (4)2
(2) 2 • 12
Factors as Squares
6 • (3) 2
Factors as Squares
2 • (5) 2
3) The diagram below is a visual model representing “square number” progression. Draw the next picture of
the sequence in your notebook and explain the pattern.
The number of dots on each picture corresponds with a “square number” created by squaring the
number that represents where the figure is in the sequence of pictures. The 5th picture should
have 25 dots, as (5)2 = 25 .
4) The diagram below is a visual model representing “square number” progression. Draw the next picture of
the sequence in your notebook and explain the pattern.
The number of triangles in each picture corresponds with a “square number” created by squaring
the number that represents where the figure is in the sequence of pictures. The 4th picture should
have 16 dots, as (4) 2 = 16 .
5) Inverse operations: The inverse of addition is subtraction. What is the inverse of multiplication?
The inverse of multiplication is division.
6) The inverse of a square number is the square root. Find the square root of each square number below, by
first placing the number under a radical and then showing your work as in the example.
b) Square root of 49
c) Square root of 81
d) Square root of 121
a) Square root of 25
25 = 52 = 5
49 = 7 2 = 7
81 = 92 = 9
7) Vocabulary: Define these terms in your own words…
Square Number
Square Root
Radical
The result of squaring a
The inverse operation to
The symbol (
) that
number.
squaring a number.
represents the operation
of finding a square root.
121 = 112 = 11
Factors
Quantities that, when
multiplied together, create
a product.
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