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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 : **

**1 ^{st}** tank volume,

= (3)^{3}

= 27 m^{3}

**2 ^{nd}** tank volume,

= (1.5)^{3}

= 3.375 m^{3}

Thus, 1^{st} 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

= 27x^{3} + 125x^{3} + 64x^{3} = 729000

= 216x^{3} = 729000

= x^{3} = 3375

= x = 3√3375

= 15

**∴** 1^{st} number = 45

**∴** 2^{nd} number = 60

**∴** 3^{rd} 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) 1 ^{st }2,74, 2^{nd}625**

**∴ **∛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 1^{st} tank = 43000

**∴** Side = ∛343000

= √70 × 70 × 70

= 70 cm

2^{nd} tank side = ∛42875

= ∛35 × 35 × 35

= 35 cm.

Therefore, 1^{st} tank occupy more space.

**Next Chapter Solution : **

👉 Chapter 5 👈