Cubes and Cube Roots Class 8 Notes | EduRev

Mathematics (Maths) Class 8

Class 8 : Cubes and Cube Roots Class 8 Notes | EduRev

 Page 1


Q u e s t i o n : 1
Evaluate:
i
8
3
ii
15
3
iii
21
3
iv
60
3
S o l u t i o n :
i
8
3
 = (8 ×8 ×8)
= 512.
Thus, the cube of 8 is 512.
ii
15
3 
= (15 ×15 ×15)
= 3375.
Thus, the cube of 15 is 3375.
iii
21
3 
= (21 ×21 ×21)
= 9261.
Thus, the cube of 21 is 9261.
iv
60
3 
= (60 ×60 ×60)
= 216000.
Thus, the cube of 60 is 216000.
Q u e s t i o n : 2
Evaluate:
i
1.2
3
ii
3.5
3
iii
0.8
3
iv
0.05
3
S o l u t i o n :
i
Page 2


Q u e s t i o n : 1
Evaluate:
i
8
3
ii
15
3
iii
21
3
iv
60
3
S o l u t i o n :
i
8
3
 = (8 ×8 ×8)
= 512.
Thus, the cube of 8 is 512.
ii
15
3 
= (15 ×15 ×15)
= 3375.
Thus, the cube of 15 is 3375.
iii
21
3 
= (21 ×21 ×21)
= 9261.
Thus, the cube of 21 is 9261.
iv
60
3 
= (60 ×60 ×60)
= 216000.
Thus, the cube of 60 is 216000.
Q u e s t i o n : 2
Evaluate:
i
1.2
3
ii
3.5
3
iii
0.8
3
iv
0.05
3
S o l u t i o n :
i
1.2
3
 = (1. 2 ×1. 2 ×1. 2)
= 1.728
Thus, the cube of 1.2 is 1.728.
ii
3.5
3
= (3. 5 ×3. 5 ×3. 5)
= 42.875
Thus, the cube of 3.5 is 42.875.
iii
0.8
3
= (0. 8 ×0. 8 ×0. 8)
= 0.512
Thus, the cube of 0.8 is 0.512.
iv
0.05
3
= (0. 05 ×0. 05 ×0. 05)
= 0.000125
Thus, the cube of 0.05 is 0.000125.
Q u e s t i o n : 3
Evaluate:
i
4
7
3
ii
10
11
3
iii
1
15
3
iv
1
3
10
3
S o l u t i o n :
i
 
(
4
7
)
3
=
(
4
7
×
4
( )
( )
( )
( )
Page 3


Q u e s t i o n : 1
Evaluate:
i
8
3
ii
15
3
iii
21
3
iv
60
3
S o l u t i o n :
i
8
3
 = (8 ×8 ×8)
= 512.
Thus, the cube of 8 is 512.
ii
15
3 
= (15 ×15 ×15)
= 3375.
Thus, the cube of 15 is 3375.
iii
21
3 
= (21 ×21 ×21)
= 9261.
Thus, the cube of 21 is 9261.
iv
60
3 
= (60 ×60 ×60)
= 216000.
Thus, the cube of 60 is 216000.
Q u e s t i o n : 2
Evaluate:
i
1.2
3
ii
3.5
3
iii
0.8
3
iv
0.05
3
S o l u t i o n :
i
1.2
3
 = (1. 2 ×1. 2 ×1. 2)
= 1.728
Thus, the cube of 1.2 is 1.728.
ii
3.5
3
= (3. 5 ×3. 5 ×3. 5)
= 42.875
Thus, the cube of 3.5 is 42.875.
iii
0.8
3
= (0. 8 ×0. 8 ×0. 8)
= 0.512
Thus, the cube of 0.8 is 0.512.
iv
0.05
3
= (0. 05 ×0. 05 ×0. 05)
= 0.000125
Thus, the cube of 0.05 is 0.000125.
Q u e s t i o n : 3
Evaluate:
i
4
7
3
ii
10
11
3
iii
1
15
3
iv
1
3
10
3
S o l u t i o n :
i
 
(
4
7
)
3
=
(
4
7
×
4
( )
( )
( )
( )
7
×
4
7
)
=
(
64
343
)
Thus, the cube of
(
4
7
)
 is
(
64
343
)
.
(ii)  
(
10
11
)
3
=
(
10
11
×
10
11
×
10
11
)
=
(
1000
1331
Page 4


Q u e s t i o n : 1
Evaluate:
i
8
3
ii
15
3
iii
21
3
iv
60
3
S o l u t i o n :
i
8
3
 = (8 ×8 ×8)
= 512.
Thus, the cube of 8 is 512.
ii
15
3 
= (15 ×15 ×15)
= 3375.
Thus, the cube of 15 is 3375.
iii
21
3 
= (21 ×21 ×21)
= 9261.
Thus, the cube of 21 is 9261.
iv
60
3 
= (60 ×60 ×60)
= 216000.
Thus, the cube of 60 is 216000.
Q u e s t i o n : 2
Evaluate:
i
1.2
3
ii
3.5
3
iii
0.8
3
iv
0.05
3
S o l u t i o n :
i
1.2
3
 = (1. 2 ×1. 2 ×1. 2)
= 1.728
Thus, the cube of 1.2 is 1.728.
ii
3.5
3
= (3. 5 ×3. 5 ×3. 5)
= 42.875
Thus, the cube of 3.5 is 42.875.
iii
0.8
3
= (0. 8 ×0. 8 ×0. 8)
= 0.512
Thus, the cube of 0.8 is 0.512.
iv
0.05
3
= (0. 05 ×0. 05 ×0. 05)
= 0.000125
Thus, the cube of 0.05 is 0.000125.
Q u e s t i o n : 3
Evaluate:
i
4
7
3
ii
10
11
3
iii
1
15
3
iv
1
3
10
3
S o l u t i o n :
i
 
(
4
7
)
3
=
(
4
7
×
4
( )
( )
( )
( )
7
×
4
7
)
=
(
64
343
)
Thus, the cube of
(
4
7
)
 is
(
64
343
)
.
(ii)  
(
10
11
)
3
=
(
10
11
×
10
11
×
10
11
)
=
(
1000
1331
)
Thus, the cube of
(
10
11
)
 is
(
1000
1331
)
.
(iii)  
(
1
15
)
3
=
(
1
15
×
1
15
×
1
15
)
=
(
1
3375
)
Thus, the cube of
(
1
15
)
 is
Page 5


Q u e s t i o n : 1
Evaluate:
i
8
3
ii
15
3
iii
21
3
iv
60
3
S o l u t i o n :
i
8
3
 = (8 ×8 ×8)
= 512.
Thus, the cube of 8 is 512.
ii
15
3 
= (15 ×15 ×15)
= 3375.
Thus, the cube of 15 is 3375.
iii
21
3 
= (21 ×21 ×21)
= 9261.
Thus, the cube of 21 is 9261.
iv
60
3 
= (60 ×60 ×60)
= 216000.
Thus, the cube of 60 is 216000.
Q u e s t i o n : 2
Evaluate:
i
1.2
3
ii
3.5
3
iii
0.8
3
iv
0.05
3
S o l u t i o n :
i
1.2
3
 = (1. 2 ×1. 2 ×1. 2)
= 1.728
Thus, the cube of 1.2 is 1.728.
ii
3.5
3
= (3. 5 ×3. 5 ×3. 5)
= 42.875
Thus, the cube of 3.5 is 42.875.
iii
0.8
3
= (0. 8 ×0. 8 ×0. 8)
= 0.512
Thus, the cube of 0.8 is 0.512.
iv
0.05
3
= (0. 05 ×0. 05 ×0. 05)
= 0.000125
Thus, the cube of 0.05 is 0.000125.
Q u e s t i o n : 3
Evaluate:
i
4
7
3
ii
10
11
3
iii
1
15
3
iv
1
3
10
3
S o l u t i o n :
i
 
(
4
7
)
3
=
(
4
7
×
4
( )
( )
( )
( )
7
×
4
7
)
=
(
64
343
)
Thus, the cube of
(
4
7
)
 is
(
64
343
)
.
(ii)  
(
10
11
)
3
=
(
10
11
×
10
11
×
10
11
)
=
(
1000
1331
)
Thus, the cube of
(
10
11
)
 is
(
1000
1331
)
.
(iii)  
(
1
15
)
3
=
(
1
15
×
1
15
×
1
15
)
=
(
1
3375
)
Thus, the cube of
(
1
15
)
 is
(
1
3375
)
(iv) 1
3
10
3
= 
(
13
10
)
3
=
(
13
10
×
13
10
×
13
10
)
=
(
2197
1000
)
Thus, the cube of 1
3
10
is 
(
2197
1000
)
. 
Q u e s t i o n : 4
Which of the following numbers are perfect cubes? In case of perfect cube, find the number whose cube is the
given number.
i
125
ii
( )
( )
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