9.1 square roots day 1

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