Download Perfect Squares and Square Roots

Perfect Squares and Square Roots
You will learn:
1. that a perfect square is a whole number whose square root is a whole number (for example is 5,
thus, 25 is a perfect square.)
2. to identify the perfect squares from 0 to 100 by squaring the whole numbers from 0 to 10;
3. the square root of a number is that number which when multiplied by itself equals the number;
4. that any whole number other than a perfect square has a square root that lies between two
consecutive whole numbers;
5. to identify the two consecutive whole numbers between which the square root of a given
whole number from 0 to 100 lies;
6. that the square root of a whole number that is not a perfect square is an irrational number; (for
example 2 is an irrational number.) (An irrational number cannot be expressed exactly as a
ratio.)
7. To use a calculator to find square roots.
Vocabulary
1. Perfect squares are the squares of the whole numbers.
2. The opposite of squaring a number is finding its square root.
3. A radical sign (
) is the symbol for square root.
4. Irrational numbers are numbers that can not be represented by a ratio of two integers.
Irrational numbers can be represented by decimals that do not end and are not repeating. For
example, 0.34334334… is an irrational number.
Team Activity 1: Use 9 tiles to make a square. What did you discover? Try 16 tiles. Is your
conclusion the same?
EXAMPLE 1:
Square 1: = 1 x 1 = 1
a perfect square
Square 2: = 2 x 2 = 4
a perfect square
List the other perfect squares. Write answers on this paper.
1
12
1x1
1
2
22
2x2
4
3
32
3x3
9
4
5
6
7
8
9
10
You can square a number using a calculator.
Find Perfect Squares Using a Calculator.
EXAMPLE 2: Find Perfect Squares Using a Calculator.
12
13
Finding the Square Root of a Perfect Square
Find the square root of each integer.
Using the calculator…
1. Enter 100
2. Press the square root key.
14
100
100
81
81
64
64
36
36
16
16
4
4
25
25
49
49
9
9
1
1
Example: Find the square root of
36
.
100
10
36
36
is the same as
. The square root of a fraction is the same as the square
100
100
root of the numerator over the square root of the denominator.
1. Find the square root of the numerator. 36 = 6.
2. Find the square root of the denominator. 100 = 10
6 3
3. Write and simplify it.
=
10 5
Try it 2. Find the square root of
9
and
36
16
.
64
Estimating Square Roots that are Not Perfect Squares
EXAMPLE: Between what two consecutive whole numbers does 12 lie?
1. Find the perfect square numbers it lies between.
2. 12 lies between 9 and 16.
3. The square root of 9 = 3 and the square root of 16 = 4 lies between the two
consecutive whole numbers 3 and 4.
Try it 1. Between what two consecutive whole numbers does each number lie?
72
5
54