5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

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5.5 Roots of Real 5.5 Roots of Real Numbers Numbers Squares Roots Squares Roots Nth Roots Nth Roots Principal Roots Principal Roots

Transcript of 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Page 1: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

5.5 Roots of Real 5.5 Roots of Real NumbersNumbers

Squares RootsSquares Roots

Nth RootsNth Roots

Principal RootsPrincipal Roots

Page 2: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Square Roots

Since 42 = 16, then but (-4)2 = 16.

So the square root of 16 is 4 and -4?

The Principal root is 4.

The Principal root are always positive.

416

Page 3: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Cube roots

53 = 125 , soHere are the parts of a root

Square roots have index 2, which is not shown

51253

Page 4: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

N th root

There are more roots then square or cubes.

abthenbaIf nn ,

3243;2433 55

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How do I know if the answer is positive or negative

For example:

In case of numbers we take the principle root “5”

When solve an equation

x2 = 25, you take the square root of both sides. Since Square roots are even “2”, the answer is 5 and -5

5525 or

Page 6: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Even roots the answer have to come out positive

Even roots

Odd roots

55255 2

282 33 3

3273

Page 7: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Other Roots

Some we will work with later in this class.

numbersimagineryyougives

n

16

00

Page 8: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

The ± symbol

± means positive and negative

So

Since x2 is positive, it does not have to be in an absolute value

24 864 xx

Page 9: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Simplify

43 5 p

Page 10: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Simplify

23

43

5

5

p

p

Page 11: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Simplify

5 1510243 ba

Page 12: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Simplify

32

5 1510

3

243

ba

ba

Page 13: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Simplify

4

Page 14: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Simplify

6 6a

Page 15: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Simplify

a

a6 6

Page 16: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Simplify

5 152243 x

Page 17: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Simplify

3

5 15

23

2243

x

x

Page 18: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

How do you use your Calculator to find the values

It depends on your calculator, normal it is function you can find with your shift button.

We will have to find it on your calculator.

Find the approximate value of

3 38

Page 19: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

How do you use your Calculator to find the values

It depends on your calculator, normal it is function you can find with your shift button.

We will have to find it on your calculator.

Find the approximate value of

362.3361975407.3383

Page 20: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

HomeworkHomework

Page 248 – 249 Page 248 – 249

#17 – 55 odd, 63#17 – 55 odd, 63

Page 21: 5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

HomeworkHomework

Page 248Page 248

#16 – 58 even#16 – 58 even


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