Cubes and Cube-Roots ICSE Class-8th Concise Mathematics Selina Solutions Chapter-4. We provide step by step Solutions of Exercise / lesson-4 Cubes and Cube-Roots ICSE Class-8th Concise Selina Mathematics. Our Solutions contain all type Questions with Exe-4A , Exe-4 B ,  to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8.

## Cubes and Cube-Roots ICSE Class-8th Concise Mathematics Selina Solutions Chapter-4

–: Select Topics :–

Exercise-4 A ,

Exercise-4 B

### Exercise- 4 A Cubes and Cube-Roots ICSE Class-8th Concise

#### Question 1 :-

Find the cube of :
(i) 7
(ii) 11
(iii) 16
(iv) 23
(v) 31
(vi) 42
(vii) 54

#### Question 2 :-

Find which of the following are perfect cubes :
(i) 243
(ii) 588
(iii) 1331
(iv) 24000
(v) 1728
(vi) 1938

(i) 243

 3 243 3 81 3 27 3 9 3 3 1

∵ 243 = 3 x 3 x 3 x 3 x 3
= (3 x 3 x 3) x 3 x 3
= 33 x 3 x 3
∴ 279 is not a perfect cube.

(ii) 588

 2 588 2 294 7 147 7 21 3 3 1

588 = 2 x 2 x 7 x 7 x 3

∴ 588 is not perfect cube.

(iii) 1331

 11 1331 11 121 11 11 1

∴ 1331 = 11 x 11 x 11 = (11)3
∴ 1331 is a perfect cube.

(iv) 24000

∵ 24000 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5
= (2)2 x (2)3 x (5)3 x 3
∴ 24000 is not a perfect cube.

(v) 1728

 2 1728 2 864 2 432 2 216 2 108 2 54 3 27 3 9 3 3 1

∵ 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
= (2)3 x (2)3 x (3)3
∵  1728 is a perfect cube.

(vi) 1938

 2 1938 3 936 17 323 19 19 1

1938 = 2 x 3 x 17 x 19
1938 is not a perfect cube.

#### Question 3 :-

Find the cubes of :
(i) 2.1
(ii) 0.4
(iii) 1.6
(iv) 2.5
(v) 0.12
(vi) 0.02
(vii) 0.8

(i) 2.1

= (2.1)3

= 9.261

(ii) 0.4

= (0.4)3

= 0.064

(iii) 1.6

= (1.6)3

= 4.906

(iv) 2.5

= (2.5)3

= 15.625

(v) 0.12

= (0.12)3

= 0.001728

(vi) 0.02

= (0.02)3

= 0.00000

(vii) 0.8

= (0.8)3

= 0.512

#### Question 4 :-

Find the cubes of :
(i) 3/7
(ii) 8/9
(iii) 10/13
(iv) 1  2/7
(v) 2  1/2

(i)

(ii)

(iii)

(iv)

(v)

#### Question 5 :-

Find the cubes of :
(i) -3
(ii) -7
(iii) -12
(iv) -18
(v) -25
(vi) -30
(vii) -50

(i) -3

= (-3)3
= -3 x -3 x -3
= -(3 x 3 x 3)
= -27

(ii) -7

= (-7)3
= -7 x -7 x -7
= -(7 x 7 x 7)
=-343

(iii) -12

= (-12)3
= -12 x -12 x -12
= -(12 x 12 x 12)
= -1728

(iv) -18

= (-18)3
= -18 x -18 x -18
= -(18 x 18 x 18)
= -5832

(v) -25

= (-25)3
= -25 x -25 x -25
= -(25 x 25 x 25)
= -15625

(vi) -30

= (-30)3
= -30 x -30 x -30
= -(30 x 30 x 30)
= -27000

(vii) -50

= (-50)3
= -50 x -50 x -50
= -(50 x 50 x 50)
= -125000

#### Question 6 :-

Which of the following are cubes of:
(i) an even number
(ii) an odd number
216, 729, 3375, 8000, 125, 343, 4096 and 9261.

(i) an even number :

∵ 216 = 2 x 2 x 2 x 3 x 3 x 3

 2 216 2 108 2 54 3 27 3 9 3 3 1

= (2)3 x (3)3
= (6)3

∵ 729 = 3 x 3 x 3 x 3 x 3 x 3

 3 729 3 243 3 81 3 27 3 9 3 3 1

= (3)3 x (3)3
= (9)3

∵ 3375 = 5 x 5 x 5 x 3 x 3 x 3

 5 3375 5 675 5 135 3 27 3 9 3 3 1

= (5)3 x (3)3
= (15)3

∵ 8000 = 20 x 20 x 20
= (20)3

 5 125 5 25 5 5 1

125 = 5 x 5 x 5
= (5)3

∵ 343 = 7 x 7 x 7
= (7)3

 7 343 7 49 7 7 1

∵ 4096 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

 2 4096 2 2048 2 1024 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1

= (2)3 x (2)3 x (2)3 x (2)3
=(16)3
Cubes of an even number are 216, 8000, 4096.

(ii) an odd number :

∵ 216 = 2 x 2 x 2 x 3 x 3 x 3

 2 216 2 108 2 54 3 27 3 9 3 3 1

= (2)3 x (3)3
= (6)3

∵ 729 = 3 x 3 x 3 x 3 x 3 x 3

 3 729 3 243 3 81 3 27 3 9 3 3 1

= (3)3 x (3)3
= (9)3

∵ 3375 = 5 x 5 x 5 x 3 x 3 x 3

 5 3375 5 675 5 135 3 27 3 9 3 3 1

= (5)3 x (3)3
= (15)3

∵ 8000 = 20 x 20 x 20
= (20)3

 5 125 5 25 5 5 1

125 = 5 x 5 x 5
= (5)3

∵ 343 = 7 x 7 x 7
= (7)3

 7 343 7 49 7 7 1

∵ 4096 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

 2 4096 2 2048 2 1024 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1

(2)3 x (2)3 x (2)3 x (2)3

=(16)3

Cubes of an odd number are 729, 3375, 125, 343, 9261.

#### Question 7 :-

Find the least number by which 1323 must be multiplied so that the product is a perfect cube.

The prime factor of 1323 are =3 x 3 x 3 x 7 x 7
= (3 x 3 x 3) x 7 x 7
Clearly, 1323 must be multiplied by 7.

#### Question 8 :-

Find the smallest number by which 8768 must be divided so that the quotient is a perfect cube.

The prime factor of 8768 are

 2 8768 2 4384 2 2192 2 1096 2 548 2 274 137 137 1

= 2 x 2 x 2 x 2 x 2 x 2 x 137
= (2 x 2 x 2) x (2 x 2 x 2) x 137
Clearly, 8768 must be divided by 137.

#### Question 9 :-

Find the smallest number by which 27783 be multiplied to get a perfect square number.

 3 27783 3 9261 3 3087 3 1029 7 343 7 49 7 7 1

= 3 x 3 x 3 x 3 x 7 x 7 x 7
= (3 x 3 x 3) x (7 x 7 x 7) x 3
Clearly, 27783 must be multiplied by 3 x 3
= 9

#### Question 10 :-

With what least number must 8640 be divided so that the quotient is a perfect cube?

The prime factors of 8640 are

 2 8640 2 4320 2 2160 2 540 2 270 3 135 3 45 3 15 5 5 1

= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5
= (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3) x 5
Clearly, 8640 must be divided by 5.

#### Question 11 :-

Which is the smallest number that must be multiplied to 77175 to make it a perfect cube?

The prime factor of 77175 are

 3 77175 3 25725 5 8575 5 1715 7 343 7 49 7 7 1

= 3 x 3 x 5 x 5 x 7 x 7 x 7
= (7 x 7 x 7) x 3 x 3 x 5 x 5
Clearly, 77175 must be multiplied by 3 x 5
= 15

### Exercise – 4 B Selina Solutions Cubes and Cube-Roots for ICSE Class-8th

#### Question 1 :-

Find the cube-roots of :
(i) 64
(ii) 343
(iii) 729
(iv) 1728
(v) 9261
(vi) 4096
(vii) 8000
(viii) 3375

(i) 64

= ³√643
= (2 x 2 x 2) x (2 x 2 x 2)
= 2 x 2
= 4

 2 64 2 32 2 16 2 8 2 4 2 2 1

(ii) 343

= ³√343
= 7 x 7 x 7 = 7

 7 343 7 49 7 7 1

(iii) 729

=  ³√729
= (3 x 3 x 3) x (3 x 3 x 3)
= 3 x 3
=9

 3 729 3 243 3 81 3 27 3 9 3 3 1

(iv) 1728

= ³√1728
= (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3)
= 2 x 2 x 3
=12

 2 1728 2 864 2 432 2 216 2 108 2 54 3 27 3 9 3 3 1

(v) 9261

=  ³√9261
= (3 x 3 x 3) x (7 x 7 x 7)
= 3 x 7
= 21

 3 9261 3 3087 3 1029 7 343 7 49 7 7 1

(vi) 4096

= ³√4096
= (2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2)
= 2 x 2 x 2 x 2
= 16

 2 4096 2 2048 2 1024 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1

(vii) 8000

= ³√8000
= (4 x 4 x 4) x (5 x 5 x 5)
= 4 x 5
=20

 4 8000 4 2000 4 500 5 125 5 25 5 5 1

(viii) 3375

=  ³√3375
= (5 x 5 x 5) x (3 x 3 x 3)
= 5 x 3
= 15

 5 3375 5 675 5 135 5 27 3 9 3 3 1

#### Question 2 :-

Find the cube-roots of :
(i) 27/ 64
(ii) 125/216
(iii) 343/512
(iv) 64 x 729
(v) 64 x 27
(vi) 729 x 8000
(vii) 3375 x 512

(i)

(ii)

(iii)

(iv) 64 x 729

(v) 64 x 27

= 4 x 3
= 12

(vi) 729 x 8000

= 9 x 20
= 180
(vii) 3375 x 512

= 15 x 8
= 120

#### Question 3 :-

Find the cube-roots of :
(i) -216
(ii) -512
(iii) -1331
(iv) -27/125
(v) -64/343
(vi) -5`12/343
(vii) -2197
(viii) -5832
(ix) -2744000

(i) -216

= -6

(ii) -512

= ³√-512
= √-8×-8×-8
= -8

(iii) -1331

= ³√-1331
= √-11×-11×-11
= -11

(iv)

(v)

(vi)

(vii) -2197

= ³√-2197

 13 2197 13 169 13 13 1

= ³√-13×-13×-133
= -13

(viii) -5832

= ³√-5832

 2 5832 2 2916 2 1458 3 729 3 243 3 81 3 27 3 9 3 3 1

= √-2×-2×-2×-3×-3×-3×-3×-3×-3

= – 2 x -3 x -3
= -18

(ix) -2744000

= ³√-2744000

 2 2744000 2 1372000 2 686000 7 343000 7 49000 7 7000 10 1000 10 100 10 10 1

= √-2×-2×-2×-7×-7×-7×-10×-10×-10
= -2 x -7 x -10
= -140

#### Question 4:-

Find the cube-roots of :
(i) 2.744
(ii) 9.261
(iii) 0.000027
(iv) -0.512
(v) -15.625
(vi) -125 x 1000

(i) 2.744

 2 2744 2 1372 2 686 7 343 7 49 7 7 1

(ii) 9.261

 3 9261 3 3087 3 1029 7 343 7 49 7 7 1

(iii) 0.000027

(iv) -0.512

= -0.8

(v) -15.625

= – 2.5

 5 15625 5 3125 5 625 5 125 5 25 5 5 1

(vi) -125 x 1000

= √-125×100

= √-(5×5×5)×(10×10×10)

= -5 x 10

= -50

#### Question 5 :-

Find the smallest number by which 26244 may be divided so that the quotient is a perfect cube.

The prime factors of 26244 are

 2 26244 2 13122 3 6561 3 2187 3 729 3 243 3 81 3 27 3 9 3 3 1

=  2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3
= (3 x 3 x 3) x (3 x 3 x 3) x 3 x 3 x 2 x 2
Clearly, 26244 must be divided by
3 x 3 x 2 x 2 = 36

#### Question 6 :-

What is the least number by which 30375 should be multiplied to get a perfect cube?

The prime factors of 30375 are

 3 30375 3 10125 3 3375 3 1125 3 375 5 125 5 25 5 5 1

= 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5
= (3 x 3 x 3) x (5 x 5 x 5) x 3 x 3
Clearly, 30375 must be multiplied with 3

#### Question 7 :-

Find the cube-roots of :
(i) 700 x 2 x 49 x 5
(ii) -216 x 1728
(iii) -64 x -125
(iv) -27/343
(v) 729/1331
(vi) 250.047
(vii) -175616

(i) 700 x 2 x 49 x 5

 2 700 2 350 5 175 5 35 7 7 1

=  2 x 2 x 5 x 5 x 7 x 2 x 7 x 7 x  5
= (2 x 2 x 2) x (5 x 5 x 5) x (7 x 7 x 7)
= 2 x 5 x 10
=70

(ii) -216 x 1728

 2 216 2 108 2 54 3 27 3 9 3 3 1

 2 1728 2 864 2 432 216

= -(2 x 2 x 2 x 3 x 3 x 3) x (2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3)

= -2 x 3 x 2 x 2 x 3
= -72

(iii) -64 x -125

-64 x -125
= -(4 x 4 x 4) x -(5 x 5 x5)
= -4 x -5
= 20

(iv)

(v)

(vi) 250.047

= 250047/1000

 3 250047 3 83349 3 27783 3 9261 3 3087 3 1029 7 343 7 49 7 7 1

= 6.3

(vii) -175616

 2 175616 2 27808 2 43904 2 21952 2 10976 2 5488 2 2744 2 1372 2 686 7 343 7 49 7 7 1

= -[(2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2) x (7 x 7 x 7)] =-[2 x 2 x 2 x 7] = -56

— End of Cubes and Cube-Roots Solutions :–

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