ML Aggarwal Cubes and Cube Roots Check Your Progress Class 8 ICSE Ch-4 Maths Solutions. We Provide Step by Step Answer of Check Your Progress 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 Check Your Progress 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 Check Your Progress |

Edition | 2023-2024 |

**Cubes and Cube Roots Check Your Progress**

**ML Aggarwal Class 8 ICSE Maths Solutions**

Page-78

**Question 1. Show that each of the following numbers is a perfect cube. Also, find the number whose cube is the given number:**

(i) 74088

(ii) 15625

**Answer:**

**(i) 74088**

= 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7

And, after grouping the same kind of prime factors in 3’s, its seen that no factor has been left ungrouped.

74088 = (2 × 2 × 2) × (3 × 3 × 3) × (7 × 7 × 7)

74088 is a perfect cube and its cube root is 2 × 3 × 7 = 42.

**(ii) 15625**

= 5 × 5 × 5 × 5 × 5 × 5

And, after grouping the same kind of prime factors, its seen that no factor is left ungrouped.

15625 = (5 × 5 × 5) × (5 × 5 × 5)

15625 is a perfect cube and its cube root is 5 × 5 = 25.

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

(i) -17

(ii) −3 (4/9)

**Answer:**

**(i) Cube of -17**

= (-17) × (-17) × (-17)

##### = -4913

**(ii) Cube of −3 (4/9)**

= -31/9 is

= (-31/9) x (-31/9) x (-31/9)

= -29791/729

= -40(631/729)

**Question 3. Find the cube root of each of the following numbers by prime factorisation:**

(i) 59319

(ii) 21952

**Answer:**

**(i) Cube root of ****59319**

**(ii) Cube root of 21952**

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

(i) -9261

(ii) 2 (43/343)

(iii) 0.216

**Answer:**

**(i) -9261**

= -3 x 7 = -21

**Question 5. Find the smallest number by which 5184 should be multiplied so that product is a perfect cube. Also find the cube root of the product.**

**Answer:**

5184 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

After grouping the same kind of prime factors is 3’s, its seen that one factor 3 is left ungroup.

5184 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × 3

So, in order to complete it in 3’s, we must multiply the factors 3 × 3 i.e. equal to 9.

Thus, the required smallest number that should be multiplied to 5184 so that product is a perfect cube is 9.

The cube root of 5184 × 9 = 46656 is

= 2 × 2 × 3 × 3 = 36.

**Question 6. Find the smallest number by which 8788 should be divided so that quotient is a perfect cube. Also, find the cube root of the quotient.**

**Answer:**

8788 = 2 × 2 × 13 × 13 × 13

On grouping of the same kind of factors, it’s seen that 2 × 2 has been left ungrouping.

8788 = 2 × 2 × (13 × 13 × 13)

So, 2 × 2 = 4 is the least number by which 8788 should be divided so that quotient is a perfect cube.

Hence, 8788 ÷ 4 = 2197 and its cube root = 13.

**Question 7. Find the side of a cube whose volume is 4096 m**^{3}.

^{3}.

**Answer:**

Volume of a cube = 4096 m^{3}

— : End of ML Aggarwal Check Your Progress Class 8 ICSE Maths Solutions :–

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

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