Download - Radicals are in simplest form when: No factor of the radicand is a perfect square other than 1.No factor of the radicand is a perfect square other than.

Radicals are in simplest form when:

•No factor of the radicand is a No factor of the radicand is a perfect square other than 1.perfect square other than 1.

•The radicand contains no The radicand contains no fractionsfractions

•No radical appears in the No radical appears in the denominator of a fractiondenominator of a fraction

Perfect Squares

1

4

916

253649

64

81

100121

144169196

225

256

324

400

625

289

Multiplication property of square roots:

Division property of square Division property of square roots:roots:

baab

b

a

b

a

4

16

25

100

144

= 2

= 4

= 5

= 10

= 12

To Simplify Radicals you must make sure that you do not leave any

perfect square factors under the radical sign.

*Think of the factors of the radicand that are perfect squares.

8

Perfect Square Factor * Other Factor

= 2*4 = 22

LEA

VE

IN

RA

DIC

AL

FO

RM

20

32

75

40

= =

=

=

5*4

2*16

3*25

10*4

= =

=

=

52

24

35

102

Perfect Square Factor * Other FactorLE

AV

E I

N R

AD

ICA

L F

OR

M

48

80

50

125

450

=

= =

=

=

3*16

5*16

2*25

5*25

2*225

=

=

=

=

=

34

54

25

55

215

Perfect Square Factor * Other Factor

LE

AV

E I

N R

AD

ICA

L F

OR

M

If you cannot think of any factors that are perfect squares – prime factor the radicand to see if you have any repeated factors

EX: 20 20

2 10

2 5

52

You can simplify radicals that have

variables TOO!

2x xx* == x4x = xxxx *** =

2x

46 yx =





Multiply Square Roots

REMEMBER THE

PRODUCT PROPERTY OF SQUARE

ROOTS:

baab

abba

OR


To multiply square roots – you multiply the radicands together

then simplify

2EX: 8* = 8*2 = 16

Simplify 16 = 4

Try These :

2 2

9

*

* 4

2 18*

Let’s try some more:

2

10

65

5

10

3 12


•Multiply the coefficients

•Multiply the radicands

•Simplify the radical.

Multiply & Simplify Practice

)32( )104(

)25( )38(

)54( )3(

)42( )53(

)103( 59

Homework Practice

)33( 52

)34( )105(

)25( )38(

)53( )2(

)46( )57(

1.

2.

3.

4.

5.





Division property of square Division property of square roots:roots:

b

a

b

a

To simplify a radicand that contains a fraction –

first put a separate radical in the numerator and denominator

25 25

36 36

Then simplify25 5

636

Try These :

16

225

100

64

16

36

49

81

Simplify:

If we have a radical left in the denominator then we

must rationalize the denominator:

20

36

20

36= =

Since we cannot leave a radical in the denominator we must multiply both the numerator and the denominator by this radical to rationalize

52

6

52

6* 5

5=

5*2

56

10

56=

Simplify: Hint – you will need to rationalize the denominator

A. B. 4 C. D. 16

5

80

Simplify Radicals

1) 1)

2)2)

3)3)

4)4)

2

6

5

3

2

43

8

6

5)

6)

7)

8)

3

92

32

10

3

185

2

8

Simplify some more:

Review writing in simplest radical

form:

1)2)3)4)

64sr

236x

23

29

100

14264 pn

5)

6)

7)

8)

9)

36

7

4

16

25

4

Review writing in simplest radical

form:

Which of the following is not a condition

of a radical expression in simplest form?

A. No radicals appear in the numerator of a fraction.

B. No radicands have perfect square factors other than 1.

C. No radicals appear in the denominator of a fraction.

D. No radicands contain fractions.

Adding and subtracting radical expressions

3 3 and 5 3 are like radicals

•You can You can only add or subtract radicals only add or subtract radicals together if they are like radicals – the together if they are like radicals – the radicands radicands MUSTMUST be the same be the same

3 3 and 3 5 are not like radicals