Download Lesson Squares and Square Roots

Lesson: Squares and Square Roots
Perfect Squares
n
n2
1
1
2
4
3
9
4
16
5
25
6
36
7
49
8
64
9
81
10
100
11
121
12
144
Square Roots
The square root of a number, x, is the number which, when multiplied by itself,
equals x.
i.e. 12 × 12 = 144, therefore 144 = 12
refers only to the positive square root.
The symbol
x could equal 12 (because 12 × 12 = 144)
OR
x could equal -12 (because -12 × -12 = 144)
If x2 = 144
so we write: x = ±12 if, in the context, it is possible that x could be negative.
Estimating Square Roots
Estimate
37
37
42.5
36
49
6
7
≈6.1
≈6.5
This linear approximation works well for numbers greater than
4 or 2.
Practice
Evaluate:
=
=
25 +
5 + 4
9
Question:
Where in BEDMAS do we
find
?
16
Answer: “E” for exponents
1
In fact:
Evaluate:
=
=
25 + 16
5 + 16
21
25 + 16
Evaluate:
25 = (25) 2
same as
=
41
≈ 6.40
(25 + 16)
(always 2 decimal places)
25 + 16
Evaluate:
=
25 + 4
=
29
≈ 5.39
(round properly!)
If the area of a square is 52 m2, what is its side length?
A = s×s
A = s2
52 = s2
s =
52
≈ 7.21 m
Homework:
(uses the opposite operation)
(not ±7.21 because the length of a
side cannot be negative)
2.5 Squares and Square Roots
# 1, 3, 6, 7ace, 8ace, 9, 11abc, 12abc, 14, 16