SQUARES AND SQUARE ROOTS
VOCABULARY
Perfect Square: when the square root is taken of a number, and the answer is
a
whole number, that number is a perfect square.
Radical sign:
means find the square root of the number inside.
 
Square: is a number with an exponent of 2.
Square root: is a number, that when multiplied by itself, equals the number
inside the square root symbol.
Squares and square roots are opposite ideas. Squaring a number
means multiplying the number by itself. Finding the square root of a
number is exactly the opposite. When you find the square root of a
number, you have the answer and you must find the problem. You must
find what number you would square, or multiply by itself, to get the number
for an answer.
is the symbol that means find the square root. It looks like a
division sign because it is a special kind of division. 82 is 8 x 8 = 64. The
square root of 64, or 64 , equals 8 because 8 x 8 = 64.
1 =1
36 = 6
4 =2
49 = 7
9 =3
64 = 8
16 = 4
81 = 9
25 = 5
100 = 10
Some squares roots are called perfect
squares because the number you need to multiply
by itself to equal the number inside the square root
symbol is a whole number. Study the following table
of these perfect squares and their square roots.
Page 1
Squares and Square Roots
Number
1
2
3
4
5
6
7
8
9
10
11
12
square
root


Square
1
4
9
16
25
36
49
64
81
100
121
144
number
 What is 49 ?
Since 7 x 7 =49,
Here is another table of squares. Notice that if
you read the table from left to right, you have
the squares. If you read the table from right to
left, you have the square roots. For example,
the square of 8 is 64 and the square root of 64
is 8.
Examples:

Find the square of 5.
The square of 5 means 52, or 5 x 5 = 25.

Find the square root of 81.
The square root of 81 means 81. Since
9 x 9 = 81, 81 = 9.
49 = 7.
 What is 15 to the second power?
15 to the second power means 152 , which means 15 x 15 = 225.
 What is 400 ?
400 means that we need to find a number times itself that equals 400.
Looking at the 4, which we know is 2 x 2, we are going to guess 20 x 20.
Yes, 20 x 20 = 400. Thus, 400 = 20.
 Find 24 x 49 .
24 means 2 to the fourth power, or 2 x 2 x 2 x 2 = 16.
7 x 7 = 49. So, 16 x 7 = 112.
49 = 7 because
 What is ( 32 + 1 )2 ?
Working inside the parenthesis first, 32 = 3 x 3 = 9. 1 = 1 because 1 x
1 = 1. So, ( 32 + 1 )2 = ( 9 + 1 )2 = ( 10 )2 = 10 x 10 = 100.
Page 2
Squares and Square Roots
Solve the following problems:
1.
2.
52
6.
49 + 22
9.
81
13.
5 + 2 x 100
4.
four squared
36
144
5.
121 +
3.
7.
8.
the square root of 0 ( 9 )2
92 x 100
10.
12.
11.
25  5
4 x 36
14.
16 x
82 x 2
15.
 144 x 
64
16.
36

62  32
17.
18.
19.
20.
63 2
13 + 72
2 x 25 + 4 x 25
2 4x
Page 3
Squares and Square Roots
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