Benchmark:H.1.1.a. Extend the properties of exponents to rational exponents.

H.1.1.a.ii. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Objectives: find all the prime factors of a number simplify radical expressions

Radicals

Because = 4 : 2 is a square root of 4

In the expression , the is the radical sign and 64 is the radicand.

22

Example1

Find the square root:

Practice1

Find the square root:

0.2

Perfect Squares

List some perfect squares.

1• 1= ____ 2•2 = ____ 3•3 = ____

4•4 = _____ 5•5 = _____ 6•6 = ____

7•7 = ____ 8•8 = _____ 9•9 = _____

10•10 = ______

1 4 9

16 25 36

49 64 81

100

The FANCY way to simplify a radical expression

Simplify :

Ugly Answer: ____________

12.1244

The FANCY way to simplify a radical expression

Simplify :

Step 1: Find a perfect square that goes into 147.

The FANCY way to simplify a radical expression

Simplify :

Step 2: Split up the radical and simplify.

The EASY way to simplify a radical expression

Factoring is a way to find ALL the prime numbers that go into a number.

A prime number can only be divided by 1 and itself.

Example 2

Find all the prime factors of 300.

300

1502

275

515

53

Practice 2

Find all the prime factors of 126.

126

632

321

37

The EASY way to simplify a radical expression

When simplifying a square root, the first step is to factor the number.

Only take 1 number from each pair outside of the radical.

Example 3: Use whiteboard to factor

Simplify the following expression:

605

1215

1111

Example 3

Simplify the following expression:

11

Example 3

Simplify the following expression:

DOUBLE CHECK!!

24.596724.5967

Practice 3

Simplify the following expression:

72

362

218

29

33

Practice 3

Simplify the following expression:

2

Practice 3

Simplify the following expression:

DOUBLE CHECK!!

8.485288.48528

Example 4

Simplify the following expression:

75

155

35

Simplify the following expression:

Example 4

Practice 4

Simplify the following expression:

90

452

59

33

Simplify the following expression:

Practice 4

Example 5

Simplify the following expression:

49

77

4 22 49a b

Simplify the following expression:

2 7 7 aaaabb

Example 5

2214a b

4 22 49a b

Practice 5

Simplify the following expression:

8

42

22

Practice 5

Simplify the following expression:

46 2x x

2x

Example 6

The formula can be used to find the size of a square sector where a is the area of the square and s is the length of a side. What is the length of the side of a square with an area of 729 sq. miles?729 = a or s?

27miles

Whiteboards!!!

Find the square root:

26

36

6

Find the square root:

29

81

9

Find the square root:

27

49

7

Draw a factor tree for: 50

50

105

25

Simplify the following expression:

5 5 2

50

5 2

5

Draw a factor tree for: 63

63

97

33

Simplify the following expression:

3 3 7

63

3 7

3