Cubes and Cube-Roots ICSE Class-8th Concise Selina

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

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–: Select Topics :–

 

Exercise-4 A ,

Exercise-4 B

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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
Answer :-

Question 2 :-

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

(i) 243

(ii) 588

588 = 2 x 2 x 7 x 7 x 3

∴ 588 is not perfect cube.

(iii) 1331

∴ 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

∵ 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

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
Answer :-

(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
Answer :-

(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
Answer :-

(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.
Answer :-

(i) an even number :

∵ 216 = 2 x 2 x 2 x 3 x 3 x 3

= (2)³ x (3)³
= (6)³

∵ 729 = 3 x 3 x 3 x 3 x 3 x 3

= (3)³ x (3)³
= (9)³

∵ 3375 = 5 x 5 x 5 x 3 x 3 x 3

= (5)³ x (3)³
= (15)³

∵ 8000 = 20 x 20 x 20
= (20)³

125 = 5 x 5 x 5
= (5)³

∵ 343 = 7 x 7 x 7
= (7)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)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)³ x (3)³
= (6)³

∵ 729 = 3 x 3 x 3 x 3 x 3 x 3

= (3)³ x (3)³
= (9)³

∵ 3375 = 5 x 5 x 5 x 3 x 3 x 3

= (5)³ x (3)³
= (15)³

∵ 8000 = 20 x 20 x 20
= (20)³

125 = 5 x 5 x 5
= (5)³

∵ 343 = 7 x 7 x 7
= (7)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)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.

Answer :-

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.
Answer :-

The prime factor of 8768 are

= 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.
Answer :-

= 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?
Answer :-

The prime factors of 8640 are

= 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?
Answer :-

The prime factor of 77175 are

= 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

 

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 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
Answer :-

(i) 64

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

(ii) 343

= ³√343
= 7 x 7 x 7 = 7

(iii) 729

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

(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

(v) 9261

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

(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

(vii) 8000

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

(viii) 3375

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
Answer :-

(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

Answer :-

(i) -216

= -6

(ii) -512

= ³√-512
= √-8×-8×-8
= -8

(iii) -1331

= ³√-1331
= √-11×-11×-11
= -11

(iv)

(v)

(vi)

(vii) -2197

(viii) -5832

(ix) -2744000

= ³√-2744000

= √-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
Answer :-

(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

(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.
Answer :-

The prime factors of 26244 are

=  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?
Answer :-

The prime factors of 30375 are

= 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
Answer :-

(i) 700 x 2 x 49 x 5

=  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 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

(vii) -175616

— End of Cubes and Cube-Roots Solutions :–

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