• DO NOW: SOLVE THE INEQUALITY BY FOLLOWING THE STEPS WE HAVE LEARNED OVER THE LAST TWO DAYS. THEN WE WILL GRAPH TOGETHER ON THE CALCULATOR;

X X2 6 1 13

HOW DO WE SIMPLIFY RADICALS?

1. simplify square roots, and

2. simplify radical expressions.

In the expression , is the radical sign and

64 is the radicand.

If x2 = y then x is a square root of y.

1. Find the square root:

8

2. Find the square root:

-0.2

64

64

0.04

11, -11

4. Find the square root:

21

5. Find the square root:

3. Find the square root: 121

441

25

815

9

6.82, -6.82

6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth.

46.5

1 • 1 = 12 • 2 = 43 • 3 = 9

4 • 4 = 165 • 5 = 256 • 6 = 36

49, 64, 81, 100, 121, 144, ...

What numbers are perfect squares?

1. Simplify

Find a perfect square that goes into 147. 147

147 349

147 349

147 7 3

2. Simplify

Find a perfect square that goes into 605.

605

121 5

121 5

11 5

Simplify

1. .

2. .

3. .

4. .

2 18

72

3 8

6 236 2

Look at these examples and try to find the pattern…

How do you simplify variables in the radical?

x7

1x x2x x3x x x4 2x x5 2x x x6 3x x

What is the answer to ? x7

7 3x x x

As a general rule, divide the exponent by two. The remainder stays in the

radical.

Find a perfect square that goes into 49.

4. Simplify 49x2

249 x7x

5. Simplify 258x254 2x

122 2x x

Simplify 369x

1. 3x6

2. 3x18

3. 9x6

4. 9x18

What are Perfect Cubes?

• 13 = 1 x 1 x 1 = 1

• 23 = 2 x 2 x 2 = 8

• 33 = 3 x 3 x 3 = 27

• 43 = 4 x 4 x 4 = 64

• 53 = 5 x 5 x 5 = 125

• and so on and on and on…..

2

2

2 x 2 = 4

3 x 3 = 9

3

3

4 x 4 = 16

4

4

5

5

5 x 5 = 25

The square root of 4 is 2

The square root of 9 is 3

The square root of 16 is 4

The square root of 25 is 5

1 23 4

5 67 8

Cubes

2

2

2

2 x 2 x 2 = 8

3 x 3 x 3 = 27

NTH ROOTS

• a square (second) root is written as:

• a cube (third) root is written as:

• a fourth root is written as: 

• a fifth root is written as: 

3

4

5

n

SIMPLIFY

3433

83

1.

2.

3. 27 33 6x y

ANSWERS

• 1. 7

• 2. -2

• 3. 3xy2

• CUBES:

Cathy is building a cubic

storage room. She wants the volume of

the space to be 1728 cubic feet. What

should the dimensions of the cube be?

ASTRONOMY A special form ofKepler’s Third Law of Planetary Motionis given by where a is theaverage distance of an object from theSun in AU (astronomical units) and P isthe period of the orbit in years. If anobject is orbiting the Sun with a periodof 12 years, what is its distance fromthe Sun?

a P 23

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