ML Aggarwal Cubes and Cube Roots Exe-4.2 Class 8 ICSE Ch-4 Maths Solutions. We Provide Step by Step Answer of Exe-4.2 Questions for Cubes and Cube Roots as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-8.

**ML Aggarwal Cubes and Cube Roots Exe-4.2 Class 8 ICSE Maths Solutions**

Board | ICSE |

Publications | Avichal Publishig Company (APC) |

Subject | Maths |

Class | 8th |

Chapter-4 | Cubes and Cube Roots |

Writer | ML Aggarwal |

Book Name | Understanding |

Topics | Solution of Exe-4.2 Questions |

Edition | 2023-2024 |

**Cubes and Cube Roots Exe-4.2**

ML Aggarwal Class 8 ICSE Maths Solutions

Page-76

**Question 1. Find the cube root of each of the following numbers by prime factorisation:**

(i) 12167

(ii) 35937

(iii) 42875

(iv) 21952

(v) 373248

(vi) 32768

(vii) 262144

(viii) 157464

**Answer :**

**(i) 12167**

**(ii) 35937**

**(iii) 42875**

**(iv) 21952**

**(v) 373248**

**(vi) 32768**

** **

**(vii) 262144**

** **

= 2 x 2 x 2 x 2 x 2 x 2 = 64

**(viii) 157464**

** **

** Question 2. Find the cube root of each of the following numbers:**

(i) -250047

(ii) -64/1331

(iii) 4(17/27)

(iv) 5(1182/2197)

**Answer :**

**(i) -250047**

**(ii) -64/1331**

**(iii) 4(17/27)**

**(iv) 5(1182/2197)**

**Question 3. Evaluate the following:**

**Answer :**

**Question 4. Find the cube root of the following decimal numbers:**

(i) 0.003375

(ii) 19.683

**Answer :**

**(i) 0.003375**

**(ii) 19.683**

**Question 5. Evaluate:**

**Answer :**

** **

= 3 + 0.2 + 0.4 = 3.6

**Question 6. Multiply 6561 by the smallest number so that product is a perfect cube. Also find the cube root of the product.**

**Answer :**

6561 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3

6561 = (3 × 3 × 3) × (3 × 3 × 3) × 3 × 3After grouping of the equal factors in 3’s, it’s seen that 3 × 3 is left ungrouped in 3’s.

In order to complete it in triplet, we should multiply it by 3.

Therefore, required smallest number = 3

and cube root of the product = 3 × 3 × 3 = 27

**Question 7. Divide the number 8748 by the smallest number so that the quotient is a perfect cube. Also, find the cube root of the quotient.**

**Answer :**

** 8748 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 × 3
**

Grouping of the equal factor in 3’s, it’s seen that 2 × 2 × 3 is left without grouping.

8748 = 2 × 2 × 3 × (3 × 3 × 3) × (3 × 3 × 3)

Therefore, on dividing the number 8748 by 12, we get 729

And, the cube root of 729 is 3 × 3 = 9.

**Question 8. The volume of a cubical box is 21952 m**^{3}. Find the length of the side of the box.

^{3}. Find the length of the side of the box.

**Answer :**

The volume of a cubical box is 21952 m^{2}.

**Question 9. Three numbers are in the ratio 3 : 4 : 5. If their product is 480, find the numbers.**

**Answer :**

Three numbers are in the ratio 3:4:5 and their product = 480

Let’s assume the numbers to be 3x, 4x and 5x, then we have

3x × 4x × 5x = 480

⇒ 60 x^{3} = 480

⇒ x^{3} = 480/60 = 8 = (2)^{3}

∴ x = 2

Hence, the number are 2 × 3, 2 × 4 and 2 × 5 = 6, 8 and 1

**Question 10. Two numbers are in the ratio 4 : 5. If the difference of their cubes is 61, find the numbers.**

**Answer :**

Two numbers are in the ratio = 4 : 5

Difference between their cubes = 61

Assume the numbers to be 4x and 5x

So, we have

(5x)^{3} – (4x)^{3} = 61

125x^{3} – 64x^{3} = 61

61x^{3} = 61

x^{3} = 1 = (1)^{3}

∴ x = 1

4x = 4 × 1 = 4 and 5x = 5 × 1 = 5

Hence, the numbers are 4 and 5

**Question 11. The difference of two perfect cubes is 387. If the cube root of the greater of two numbers is 8, find the cube root of the smaller number.**

**Answer :**

The difference in two cubes = 387

And, the cube root of the greater number = 8

So, the greater number = (8)^{3} = 8 × 8 × 8 = 512

Therefore, the second number = 512 – 387 = 125

The cube root of 125 is

= 5

— : End of ML Aggarwal Cubes and Cube Roots Exe-4.2 Class 8 ICSE Maths Solutions :–

Return to **– ML Aggarwal Maths Solutions for ICSE Class -8**

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