Warm-Up

2 2

2 2

2 2

2 2

Evaluate each expression for the given values.

Find answers to the nearest hundredth.

1.) a ; 3, 4

2.) ; 6, 10

3.) a ; 4, 7

4.) ; 3, 9

b a b

c a a c

b a b

c b b c

Warm-Up

2 2

2 2

Evaluate each expression for the given values.

Found answers to the nearest hundredth.

1.) a ; 3, 4

5

2.) ; 6, 10

b a b

c a a c

2 2

2 2

8

3.) a ; 4, 7

8.06

4.) ; 3, 9

8.49

b a b

c b b c

Homework

Questions?

Section 11.5

Square Roots of Variable Expressions

Objective

I want to be able to find square roots of variable expressions and to use them to solve equations and problems.

Please follow along…

Pg. 525

Property of Square Roots of Equal

Numbers

For any real numbers r and s:

r2 = s2 if and only if r = s or r = -s

Absolute Value and Radicals

In order to ensure the correct root is found, If n is an even positive integer, only when m is an odd positive integer.

n ma a

Example 1

Simplify.

6400 z

3

6

20

400

z

z

Example 2

Simplify.

12162 y

29

281

6

12

y

y

Example 3

Simplify.

318a 9 2

3 2

3 2

a a a

a a

a a

Example 4

Simplify.

220100 nn

n

n

10

102

Example 5

Solve.

050045 2r

3

10,

3

10 isset solution the

3

10

9

100

9

100

45

500

50045

2

2

r

r

r

Example 6

Find the length of a side of a square if its area is the same as the area of a triangle with an altitude of 24 cm and a base of 12 cm.

2 1

Define: 2

= side of square, = base of triangle,

= height of triangle

sqA s A bh

s b

h

Example 6 continued

2

2

2

112 24

2

12 24

2

144

12

The length of the side of the square is 12 cm.

sqA A

s

s

s

s

Section 11.6

The Pythagorean Theorem

Objective

I want to use the Pythagorean Theorem and its converse to solve geometric problems.

Pythagorean Theorem

In any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.

For the triangle shown, a2 + b2 = c2

a

b

c (hypotenuse)

Converse of the Pythagorean Theorem

If the sum of the squares of the lengths of the two shorter sides of a triangle is equal to the square of the length of the longest, then the triangle is a right triangle.

The right angle is the opposite the longest side,

the hypotenuse.

Example 1 One leg of a right triangle measures 36 cm. The

hypotenuse is 39 cm long. Write and solve an equation for the length of the unknown side.

?2 2 2

:

36 15 39

1521 1521

Check

2 2 2

2 2 2

2 2

2 239 36

1521 1296

225

15

a b c

b c a

b c a

b

b

b

b

Example 2a State whether or not the three given numbers could

represent the lengths of the sides of a right triangle.

16, 30, 34

a2 + b2 = c2

162 + 302 = 342

256 + 900 = 1156

1156 = 1156

Then, 16, 30, 34 could form a right triangle.

Example 2b State whether or not the three given numbers could

represent the lengths of the sides of a right triangle.

11, 11, 16

a2 + b2 = c2

112 + 112 = 162

121 + 121 = 256

242 = 256

Then, 11, 11, 16 could not form a right triangle.

Example 3 To the nearest hundredth, what is the length of a

diagonal of a rectangle whose width is 12 cm and whose length is 42 cm?

?2 2 2

:

12 42 43.68

1908 1907.94

Check

2 2 2

2 2 2

2 2

2

12 42

1908

6 53

6 53

6 7.280

43.68

a b c

a b c

c

c

c

c

c

c

And These!

Simplify. Show ALL work!

544 .)7 y

2169 .)6 b 3

5

3

363 .)9

xy

yx

10863- .)8 ca

And These!

Simplify. Show ALL work!

5 27.) 44 2 11y y y

26.) 169 13b b

5

3

2

3639.)

3

11

x y

xy

x

y

8 10 4 58.) - 63 3 7a c a c

Try These!

Find the missing length correct to the nearest hundredth.

1. a = 6, b = 8, c = ? 2. a = ?, b = 9, c = 11 3. a = 15, b = ?, c = 22 State whether or not the three given numbers

could represent the lengths of the sides of a right triangle.

4. 4, 8, 10 5. 15, 36, 39

Try These!

Find the missing length correct to the nearest hundredth.

1. a = 6, b = 8, c = 10 2. a = 6.32, b = 9, c = 11 3. a = 15, b = 16.09, c = 22 State whether or not the three given numbers

could represent the lengths of the sides of a right triangle.

4. 4, 8, 10 no 5. 15, 36, 39 yes

What About These?

Pg. 526 Oral Exercises #1-10 all

O.E. pg. 531 # 1 – 5

Clear your calculators!

2nd + 7 1 2 CLEAR ENTER

Take out your agendas!

Copy down DUE DATES!

Homework:

Sections 11.5 & 11.6 Section 11.6 Worksheet

Journal Entry

– TOPIC: Radicals in Simplest Form

– Answer the following question: Explain how to check that an expression having a square root radical is in simplest form.