squares,square roots, cubes, cube roots

8/17/2019 Squares,Square Roots, Cubes, Cube Roots

1/14

Squares

Find the value of the following

1. 23 3.2

5

2

4.2

4

31

5. 22.0

2. 2

)4(−

Numer Ste!s Solutions

1.

2

3.

4.

5.

a. "ulti!l# the numer # itself.

. Find the value.

a. For negative numers$!ut in ra%&et

and multi!l#.

. Find the value.

a. For fra%tions$multi!l# numerator andnumerator$denominator and

denomerator.

. Find the value.a. For mi'ed numer$%hange to im!ro!er

fra%tion then multi!l# as fra%tion.

. Find the value.

a. For de%imals$em!hasis on de%imal

!la%es."ulti!l# the numer # itself. . Find the value.For numer with one

de%imal !la%e$the value will e twode%imal !la%es.

%. For numer with two de%imal

!la%es$the value will e four de%imal !la%es.

Notealue for all negative numers are

!ositive.

23 3 ' 3 *

2)4(− (+4) ' (+4)1,

2

5

2

x

5

2

5

2

25

4

2

4

31

2

4

-

4

- '

4

-

1,

4*

22.0 0.2 ' 0.2 0.04

202.0 0.02 ' 0.02

0.0004


2/14

'er%ise 1

Find the value of the followings.

1. 25 3.2

5

4

5. ( ) 2

-.0−

2. ( ) 2/− 4.2

4

13

,. ( ) 2

0*.0−


1.

2

3.

4.

5.

,.

a. "ulti!l# the numer # itself.

a. Find the value.

. For negative numers$!ut in ra%&et

and multi!l#.

%. Find the value.

%. For fra%tions$multi!l# numerator andnumerator$denominator and

denomerator.

d. Find the value.%. For mi'ed numer$%hange to im!ro!er

fra%tion then multi!l# as fra%tion.

d. Find the value.

a. For de%imals$em!hasis on de%imal

!la%es."ulti!l# the numer # itself. . Find the value.For numer with one

de%imal !la%e$the value will e two

de%imal !la%es.

%. For numer with two de%imal !la%es$the value will e four de%imal

!la%es.

Square root


3/14

Find the value of the followings

1. ,4 3.1,2

32 5. 3,.0

2.1,* 4.

4112 ,. ( )

25


1.

2

3.

4.

5.

,.

a. Find the value referring to !erfe%t

square numer or refer to four

figure tale.

a. For fra%tion$find the value for thenumerator and the denominator and

write the answer as fra%tion.

a. For fra%tion that the numerator andthe denominator is not a !erfe%t

square numer$ sim!lif# to lower

term so that the# are !erfe%t squarenumer.

. Find the value for the numerator and

the denominator.rite the numer asfra%tion.

a. For mi'ed numer$ %hange it toim!ro!er fra%tion. . etermine if the numerator and the

denominator are !erfe%t square

numers.%. Find the value as in fra%tion.

a. For de%imals$%hange to fra%tion. . Find the value as in fra%tions.

%. hange the fra%tion to de%imal.

a. For square root of a square$ multi!l#the numer # itself.

. Find the square root of the answer.

Note

he answer to the square root of a square

is the numer itself.

,4 /

1,

*

1,

*4

3

1,2

32

/1

1,

/1

1,*

4

4

112

4

4*

2

-

3,.0 100

3,10

,

0.,

( )25 55 x 25 5


4/14

'er%ise 2


1. 4* 2.144

,4 3.

12/

1/ 4.

*

1- 5. 25.0 ,. ( )213


5/14


1.

2

3.

4.

5.

,.

a. Find the value referring to !erfe%tsquare numer or refer to four

figure tale.

a. For fra%tion$find the value for the

numerator and the denominator and

write the answer as fra%tion.

a. For fra%tion that the numerator and the

denominator is not a !erfe%t squarenumer$ sim!lif# to lower term so that

the# are !erfe%t square numer.

. Find the value for the numerator andthe denominator.rite the numer as

fra%tion.

a. For mi'ed numer$ %hange it to

im!ro!er fra%tion.

. etermine if the numerator and the

denominator are !erfe%t squarenumers.

%. Find the value as in fra%tion.

a. For de%imals$%hange to fra%tion.

. Find the value as in fra%tions.

%. hange the fra%tion to de%imal.

aFor square root of a square$ multi!l#the numer # itself.

. Find the square root of the answer.

ue


1. 34 2. ( )3

5− 3.3

,

5

4.3

3

12

5. 3,.0


6/14


1.

2.

3.

4.

5.

a. "ulti!l# the numer # itself 2times.

. Find the value.

a. For negative numer$!ut

ra%&et$then multi!l# the numer.

o determine the answer$multi!l#

the sign then the numer. . he answer is a negative numer.

a. .For all fra%tions$!ut ra%&et."ulti!l# the numerator and

the denominator # itself 2 times.

. etermine the value for numerator and denominator and write the

answer as fra%tion.

a. For mi'ed numer$%hange to

im!ro!er fra%tion.on6t forget the

ra%&et.

. Find the value as fra%tion aove.

a. For de%imals$ em!hasis on de%imal !la%es.For numer with one

de%imal !la%e$the value will e

three de%imal !la%es$ that is tri!leof the numer.

. Find the value and mar& thede%imal !oint %learl#.

Note

alue for all !ositive numers will e

!ositive and negative numers will enegative.

34 4 ' 4' 4 ,4

( ) 35− (+5) ' (+5) ' (+5)

+ ' ' + +5 ' 5 ' 5 125

+ 125

3

,

5

,,,

555

x x

x x

21,

125

3

3

12

3

3

-

3

3

-

333

---

x x

x x

2-

343

3,.0 0., ' 0., ' 0.,

0.21,

'er%ise 3



7/14

1. 3/ 2. ( )33− 3.3

-

2

− 4.

3

4

12

5. ( )3

5.0−


8/14


1.

2.

3.

4.

5.

%. "ulti!l# the numer # itself 2times.

d. Find the value.

%. For negative numer$ !ut ra%&et$

then multi!l# the numer.

o determine the answer$ multi!l#

the sign then the numer.d. he answer is a negative numer.

%. .For all fra%tions$ !ut ra%&et."ulti!l# the numerator and the

denominator # itself 2 times.

d. etermine the value for numerator and denominator and write the

answer as fra%tion.

%. For mi'ed numer$ %hange to

im!ro!er fra%tion. on6t forget the

ra%&et.

d. Find the value as fra%tion aove.

%. For de%imals$ em!hasis on de%imal

!la%es.For numer with onede%imal !la%e$the value will e

three de%imal !la%es$ that is tri!le

of the numer.d. Find the value and mar& the

de%imal !oint %learl#.

ue 7oot


1. 3 ,4 2. 3 125− 3. 3343

2- 4. 3

250

1, 5. 3

/

33 ,.

3-2*.0−


9/14


1.

2.

3.

4.

5.

,.

a. ue root of a numer is thenumer whi%h multi!lied twi%e

# itself !rodu%es the given

numer. . 8lternative method is redu%e

the numer to fa%tors.

%. 8nother alternative is refer to

four+figure tale or memorise !erfe%t %ue numer.

a. For all negative numers$ thevalue of %ue root will alwa#s

e negative.

a. For fra%tion$find the value for

the numerator and the

denominator. rite the answer as fra%tion.

. For fra%tion that the numerator

and the denominator is not a

!erfe%t %ue numer$sim!lif#to lower term so that the value

for numerator and denominator

%an e determine.%. rite the answer as fra%tion.

a. For mi'ed numer$%hange toim!ro!er fra%tion.

. Find the value as fra%tionaove.

a. For de%imals$ em!hasis on

de%imal !la%es.For numer

with three de%imal !la%es$thevalue will e one de%imal

!la%e.

. Find the value and mar& thede%imal !oint %learl#.

%. 8lternative method is %hange

de%imal to fra%tion.Find the%ue root as fra%tion and %hange

to de%imal as the answer.

3,4 3 444 x x 4

3,4 3 222222 x x x x x

( )3

3 4

4

3125− + 5

3

343

2- 3

---

333

x x

x x

-

3

3

250

1, 3

125

/

5

2

3

/

33 3

/

2-

2

3

3-2*.0− +0.3

3-2*.0

− 3

1000

-2*

−

+10

*

+ 0.*


10/14

'er%ise 4


1. 3 2- 2. 3 ,4− 3. 3125

/ 4. 3

12/

54

5. 32-

1-4 ,. 3 21,.0−


11/14


1.

2.

3.

4.

5.

,.

a. ue root of a numer is thenumer whi%h multi!lied twi%e

# itself !rodu%es the given

numer.a. 8lternative method is redu%e

the numer to fa%tors.

. 8nother alternative is refer to

four+figure tale or memorise !erfe%t %ue numer.

a. For all negative numers$ thevalue of %ue root will alwa#s

e negative.

a. For fra%tion$find the value for

the numerator and the

denominator. rite the answer as fra%tion.

. For fra%tion that the numerator

and the denominator is not a

!erfe%t %ue numer$sim!lif# tolower term so that the value for

numerator and denominator %an

e determine.%. rite the answer as fra%tion.

a. For mi'ed numer$%hange toim!ro!er fra%tion.

. Find the value as fra%tionaove.

a. For de%imals$ em!hasis on

de%imal !la%es.For numer with

three de%imal !la%es$the valuewill e one de%imal !la%e.

. Find the value and mar& the

de%imal !oint %learl#.%. 8lternative method is %hange

de%imal to fra%tion.Find the

%ue root as fra%tion and%hange to de%imal as the

answer.


12/14

9"7 2005 and 2004

1. Find the value of3

4

1


1

2.

a. "ulti!l# the numer # itself 2times.

. "ulti!l# the sign.

%. etermine the value for numerator and denominator

and write the answer as fra%tion

a. hange the de%imal to

fra%tion.

. Find the %ue for the

numerator and denominator.

%. hange the fra%tion to de%imal

as the answer. 1 mar& for %orre%tanswer.

2. Find the value of ( )3

512.0

9"7 2005

al%ulate the value of (4.2 : 3 2- ) 2


1. a. Find the value of the %ue root.

. ivide the two numers in the ra%&et.


13/14

%. "ulti!l# the numer # itself to

find the square of the answer.

d. etermine the de%imal !la%e.he

answer should e a two de%imal !la%es. 2 mar&s for %orre%t

answer.

9"7 2004

al%ulate the value of 4 2 ' 3/

2-−


1. a. Find the value of the square.

. Find the value of the %ue root.

%. "ulti!l# the two values #sim!lifi%ation.

d. etermine the sign of the answer.

e. 2 mar&s for %orre%t answer.

'er%ises

1.

−

3

21 3

2. 3 02-.0−


14/14

3.*

,4

4. (+0.05) 2

5. .

,. ( 2 3 + 25 ) 2

-. /3 − ; ( ) 24−

/. ( / + 3 ,4− ) 2

*.

2

1 2 ; *

squares,square roots, cubes, cube roots

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