Warm Up:
Make a perfect square chart.
Write down all the squares up to 252
12=
22=
32=
42=
52=
Keep on going….
Learn to find square roots.
Vocabulary
principal square root
perfect square
Think about the relationship between the area
of a square and the length of one of its sides.
area = 36 square units
side length = 36 = 6 units
Taking the square root of a number is the
inverse of squaring the number.
62 = 36
36 = 6
Every positive number has two square roots, one
positive and one negative.
Find the two square roots of each number.
A. 49
B. 100
C. 225
Find the two square roots of each number.
A. 0.04
B. 1.44
C. 0.49
Find the square root of each number.
9
64
25
36
-
49
81
Find the square root of each number.
**You cannot find the square root of a
negative number because no number
times itself is negative.**
A. -16
B. -289
What is solution of y2= 81
What is solution of y2= 225
What is solution of x2= 625
Hint: Squaring a number and square root are inverse operations.
Ex: 1)A square window has an area of 169
square inches. How wide is the window?
Ex: 2) A square mosaic is made of small glass
squares. If there are 196 small squares in the
mosaic, how many are along an edge?
Ex: 3) A square shaped kitchen table has an area
of 16 square feet. Will it fit through a van door
that has a 5 foot wide opening?
Evaluating Expressions
Involving Square Roots
Evaluate the expression.
𝟑 𝟑𝟔 + 𝟕
𝟐 𝟐𝟓 + 𝟒
𝟐𝟓 𝟑
+
𝟏𝟔 𝟒
Evaluating Expressions
Involving Square Roots
Evaluate the expression.
−𝟒 −𝟏𝟒 + 𝟓𝟎
𝟏𝟖 𝟏
+
𝟐
𝟒
Lesson Quiz
Find the two square roots of each number.
1. 81 9
2. 2500 50
Evaluate each expression.
3. 3 16 + 1
13
4. 7 9 – 2 49
7
5. Ms. Estefan wants to put a fence around 3 sides
of a square garden that has an area of 225 ft2.
How much fencing does she need?
45 ft
Learn to estimate square roots to a given
number of decimal places and solve
problems using square roots.
Caution!
–49 is not the same as – 49. A negative
number has no real square root.
Each square root is between two integers.
Name the integers. Explain your answer.
55
111
86
78
Each square root is between two integers.
Name the integers.
− 45
− 90
What is the approximate solution of y2 = 74
What is the approximate solution of x2 = 181
Which point is closest to 29 on the number line below?
You want to sew a fringe on a square
tablecloth with an area of 500 square
inches. Calculate the length of each side of
the tablecloth.
A 22.5 in
B 22.3 in
C 22.7 in
D 22.9 in
Elena needs to cut a square piece of wood with
an area of 69 square inches. How long should
the sides of the square be, rounded to the
nearest tenth of an inch?
aa 7 in.
.
c 34.5 in.
bb. 8.3 in.
d17.3 in.
A farmer needs to put up a square fence around
his chicken area. If the area is 91 square feet,
how much fencing is needed? Round to the
nearest whole number.
You want to build a fence around a
square garden that is 250 square feet.
Calculate the length of one side of the
garden.
A 15.1 ft
B 15.3 ft
C 15.5 ft
D 15.8 ft
Estimate:
1)
36𝑥
𝑊ℎ𝑒𝑛 𝑥 = 2
2)
10𝑥
𝑊ℎ𝑒𝑛 𝑥 = 3
Estimate:
1) 𝑎 51
2)
𝑊ℎ𝑒𝑛 𝑎 = 5
114 + 180
Compare using <,> or =:
10
5
16
4
50
8
80
9
Warm Up
Each square root is between two integers.
Name the two integers.
1.
27
2. –
456
3. Which irrational number is closest to 9?
a.
36
b.
18
c.
79
d.
60
4. A square field has an area of 324 square
feet. How long is each side of the field?
Warm Up
Evaluate each expression.
1. 8+ 144
2. 7
289
3. Barbara has a square garden with an
area of 121 square feet. How many feet of
fencing would she need for each side of the
garden?