# Maths Ace Class 8 Solutions Chapter 4

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## Maths Ace Class 8 Solutions Chapter 4 Cubes and Cube Roots

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Maths Ace Prime Class 8 Math Book, Chapter 4, Cubes and Cube Roots. Here students can easily find step by step solutions of all the problems for Cubes and Cube Roots, Exercise 4.1 and 4.2 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 4 solutions.

Cubes and Cube Roots Exercise 4.1 Solution :

Question no – (1)

Solution :

(a) 0.58

= (0.58)3

= (0.58 × 0.58 × 0.58)

= 0.195112

Hence, the cube of 0.58 is 0.195112.

(b) 46

(46)3

= (46 × 46 × 46)

= 97336

Thus, the cube of 46 is 97336

(c) (-4.5)

(-4.5)3

= (-4.5 × -4.5 × -4.5)

= -91.125

Hence, the cube of -4.5 is -91.125

(d) (9 2/5)

= (9 2/5)3

= (47/5)3

= 103823/125

Therefore, the cube of (9 2/5) is 103823/125

Question no – (2)

Solution :

(a) 108

∴ No, it is not perfect cubes

(b) 1944

1944 = 2 × 2 × 2 × 3 × 3 × 3

No it is not perfect cube

(c) 2187

2127 = 3 × 3 × 3 × 3 × 3 × 3 × 3

No, it is not perfect cube

Question no – (3)

Solution :

(a) 432

432 = 3 × 3 × 3 × 2 × 2 × 2 × 2

2 is not triplet,

To get perfect cube 432 multiply by (2 × 2) = 4

(b) Given, 37044

37044 = 3 × 3 × 3 × 7 × 7 × 7 × 2 × 2

Here, 2 is not triplet,

To get perfect cubes 37044 multiply by 2

(c) 36864

36864 = (2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3)

Here, ‘3’ is not triplet,

Hence, To get perfect cube 36864 is multiplied by ‘3’

Question no – (4)

Solution :

(a) 108

108 = 3 × 3 × 3 × 2 × 2

smallest no is 4 to be divided

(b) 1944

1944 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3

Smallest number is 9 to be divided to get perfect cube

Question no – (5)

Solution :

1st tank volume,

= (3)3

= 27 m3

2nd tank volume,

= (1.5)3

= 3.375 m3

Thus,  1st tank store more water because its volume is greater than 2nd.

Question no – (6)

Solution :

So, (6³ × 9)

= (216 × 9)

= 1944

and, (216 × 3) = 648

∴ Now, (1944 × 3)

= 5832

∴ 3√5832

= √(18 × 18 × 18)

= 18

Thus, the required number will be 18.

Question no – (7)

Solution :

Let, the no are 3x, 4x, 5x

(3x)3 + (5x)3 + (4x)3 = 729000

= 27x3 + 125x3 + 64x3 = 729000

= 216x3 = 729000

= x3 = 3375

= x = 3√3375

= 15

1st number = 45

2nd number = 60

3rd number = 75

Hence, the first number will be 45, second number will be 60 and third number will be 75.

Cubes and Cube Roots Exercise 4.2 Solution :

Question no – (1)

Solution :

(a) 2,197

By prime factorisation,

3√2197 = 3√13 × 13 × 13

= 13

(b) 5,832

3√5832 = 3√2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

= 2 × 3 × 3

= 18

(c) 3,375

3√3375 = 3√5 × 5 × 5 × 3 × 3 × 3

= 5 × 3

= 15

(d) 74,088

3√74088 = 3√2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7

= 2 × 3 × 7

= 42

Question no – (2)

Solution :

(a) 1331/2744

= ∛1331/2744

= ∛11 × 11 × 11/14 × 14 × 14

= 11/14

(b) 5832/3375

= ∛-5832/3375

= ∛- (18 × 18 × 18)/15 × 15 × 15

= – 18/15

(c) 592.704

= ∛592.704

= ∛8.4 × 8.4 × 8.4

= 8.4

(d) -185193

= ∛3√-185193

= ∛-57 × (-57) × (-57)

= -57

Question no – (3)

Solution :

(a) 1st 2,74, 2nd625

∴ ∛274625

= √65 × 65 × 65

= 65

(b) 39, 304

= ∛39304

= ∛34 × 34 × 34

= 34

(c) 4, 38, 976

= ∛438976

= ∛76 × 76 × 76

= 76

(d) 1, 03, 823

= ∛103823

= ∛47 × 47 × 47

= 47

(e) 3, 28, 509

= ∛328509

= ∛69 × 69 × 69

= 69

(f) 778, 688

= ∛778688

= ∛92 × 92 × 92

= 92

Question no – (4)

Solution :

(a) Given, 2,200

2200 = 2 × 2 × 2 × 5 × 5 × 11

5811 are not triplet

To make triplet cube, 2200 multiply with (5 × 11 × 11) = 5 × 12

= 605

(b) 1,340

2340 = 2 × 2 × 5 × 67

2, 5, 67 are not triplet

To make perfect cube, 1340 multiply with (2 × 5 × 5 × 67 × 67)

= 224450

(c) 3,378

3378 = 2 × 3 × 563

, 3, 563 are not triplet

3372 multiply by (2 × 2 × 3 × 3 × 563 × 563)

= 11410884

Question no – (5)

Solution :

Volume of cube = 8,04,357 cu. cm (given)

3√804357

= 3√93 × 93 × 93

= 93

Therefore, the Length of side of cube 39 cm.

Question no – (6)

Solution :

Volume of 1st tank = 43000

Side = ∛343000

= √70 × 70 × 70

= 70 cm

2nd tank side = ∛42875

= ∛35 × 35 × 35

= 35 cm.

Therefore, 1st tank occupy more space.

Next Chapter Solution :

Updated: June 16, 2023 — 5:30 am