9.1 square roots day 1
DESCRIPTION
TRANSCRIPT
Evaluate.
2. 92
Lesson 9.1, For use with pages 469-474
1. 52 You will NEED a calculator
from now to the end of the year!
ANSWER 25
ANSWER 81
Evaluate.
2. 92
Lesson 9.1, For use with pages 469-474
1. 52 You will NEED a calculator
from now to the end of the year!
Square Roots
9.1
Day 1
Our goals in this lesson :
To understand how to take (or find) the square root of a number
To be identify perfect squares
Essential Questions
What is the difference between an irrational number and a rational number?How are real numbers and the Pythagorean Theorem used in everyday life? What types of real-life situations could the Pythagorean Theorem or square roots apply to? Why?
VocabularyRadical Sign– The symbol for the square root
Square root – Of a number N is the number that when
multiplied by itself gives the number N. 5 and -5 are the square roots of 25 because 52=25 and (-5)2=25.
Square Roots
81
81
81
Principal Square Root
Negative Square Root
Both Square Roots
VocabularyRadical Expression– An expression that involves a radical sign
Perfect Square– Is a number with an integer square root such as
9, 16 and 25.Square root of the number must be a whole number to be a perfect square. NO decimal!
25 525 5
Perfect Squares: Area of a square = s2
Side Length of a Square12345678910
Area 1 4 9 16 25 36 49 64 81 100
These are all the perfect squares that are less than 100.
Try these examplesAre these numbers perfect squares?A) 729
B) 864
C)1444
D)1521
Try these examplesAre these numbers perfect squares?A) 729– Yes, 27
B) 864– No
C)1444 • Yes, 38.
D)1521• Yes, 39.
How do you know?
Square Roots
You can use square roots to find the side or length of a square.
Area is 144 sq. feet. What is the length of each side?
(A = s2)12 feet
Square Roots
You can use square roots to find the side or length of a square.
Area is 144 sq. feet. What is the length of each side?
The area of this square is 225 cm2
What is the length of each side?
The area of this square is 225 cm2
What is the length of each side?
15 cm
EXAMPLE 1 Evaluating Square Roots
a. 36
b. 64–
c. 425
d. 0.81
EXAMPLE 1 Evaluating Square Roots
a. 36 = 6
b. 64– = –8
c. 425
25=
d. 0.81 = 0.9
GUIDED PRACTICE for Examples 1 and 2
Find or approximate the square root to the nearest integer.
1.
4
2. 0
GUIDED PRACTICE for Examples 1 and 2
Find or approximate the square root to the nearest integer.
1.
4
2. 0
ANSWER2
ANSWER
0
GUIDED PRACTICE for Examples 1 and 2
Find or approximate the square root to the nearest integer.
3.
36–
4. 81–
GUIDED PRACTICE for Examples 1 and 2
Find or approximate the square root to the nearest integer.
3.
36–
4. 81–
ANSWER–6
ANSWER
–9
EXAMPLE 3 Using a Calculator
Evaluate the square root. Round to the nearest tenth, if necessary.
a. 56.25– b. 8 c. 1256–
SOLUTION
Keystrokes AnswerDisplay
a.
b.
c.
EXAMPLE 3 Using a Calculator
Evaluate the square root. Round to the nearest tenth, if necessary.
a. 56.25– b. 8 c. 1256–
SOLUTION
Keystrokes AnswerDisplay
a. –7.5b. 2.8c. –35.4
Simplifying radicals
16 1625 25
100400 =
100400
=1020
=
Simplifying radicals
16 1625 25
45
100400 =
100400
=1020
=12
Find two consecutive integers that each is between
29
115
82
385
5.385
10.723
9.055
19.621
Find two consecutive integers that each is between
29
115
82
385
10 11and
9 10and
19 20and
5 6and5.385
10.723
9.055
19.621
Homework
Worksheet 9.1– See page 819