Squares and Cube Roots Class 8 RS Aggarwal Exe-3E Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-3. We provide step by step Solutions of Icisce prescribed publications / writer to develp skill and confidence among students. This article is useful to learn Cubes and cube Roots of a number. Visit official Website **CISCE** for detail information about ICSE Board Class-8 Mathematics.

## Squares and Cube Roots Class 8 RS Aggarwal Exe-3E Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-3

Board | ICSE |

Publications | Goyal Brothers Prakshan |

Subject | Maths |

Class | 8th |

writer | RS Aggarwal |

Book Name | Foundation |

Ch-3 | Squares and Squire Roots , Cubes and Cube Roots |

Exe-3E | Cubes and Cube Roots of a Number |

Edition | 2024-2025 |

### Cubes and Cube Roots of a Number

(Squares and Cube Roots Class 8 RS Aggarwal Exe-3E Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-3)

**Page- 54**

**Exercise- 3E**

(Cubes and Cube Roots of a Number)

**Que-1: Find the cubes of :**

**(i) 16 (ii) 30 (iii) 1.2 (iv) 0.7 ****(v) 0.06 (vi) 2/5 (vii) 1/9 (viii) 1*(3/5)**

**Solution- **(i) 16³ = 16 x 16 x 16 = 4096

(ii) 30³ = 30 x 30 x 30 = 27000

(iii) 1,2³ = 1.2 x 1.2 x 1.2 = 1.728

(iv) 0.7³ = 0.7 x 0.7 x 0.7 = 0.343

(v) 0.06³ = 0.06 x 0.06 x 0.06 = 0.000216

(vi) (2/5)³ = 2/5 x 2/5 x 2/5 = 8/125

(vii) (1/9)³ = 1/9 x 1/9 x 1/9= 1/729

(viii) [1*(3/5)]³ = (8/5)³ = 8/5 x 8/5 x 8/5 = 512/125 = 4*(12/125)

**Que-2: Examine which of the following numbers are perfect cubes. In case of perfect of cube, find the cube root :**

**(i) 729 (ii) 1331 (iii) 5324 (iv) 3375 ****(v) 9261 (vi) 5832 (vii) 1728 (viii) 10584**

**Solution- **(i) ∛729 = ∛(3x3x3x3x3x3)

= 3 x 3 = 9.

So, it is perfect cube.

(ii) ∛1331 = ∛11x11x11

= 11.

So, it is perfect cube.

(iii) ∛5324 = It is not a perfect cube.

(iv) ∛3375 = ∛3x3x3x5x5x5

= 3 x 5 = 15

So, it is a perfect cube.

(v) ∛9261 = ∛3x3x3x7x7x7

= 3 x 7 = 21.

So, it is a perfect cube.

(vi) ∛5832 = ∛2x2x2x3x3x3x3x3x3

= 2 x 3 x 3 = 18.

So, it is a perfect cube.

(vii) ∛1728 = ∛2x2x2x2x2x2

= 2 x 2 x 3 = 12.

So, it is a perfect cube.

(viii) ∛10584 = It is not a perfect cube.

**Que-3: Find the smallest number by which 1323 must be multiplied so that the product is a perfect cube.**

**Solution-**Factorising 1323 into prime factors, 1323 = 3×3×3×7×7

Making them in groups of 3 equal factors we see that 7×7 are left.

∴ To make it into a group of 3, we have to multiply it by 7

Hence the smallest number by which it is multiplied = 7 **Ans**.

**Que-4: What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube ?**

**Solution-**Factorising 1600 into prime factors

1600 = (2×2×2×2×2×2×5×5)

Making them in groups of 3 equal factors.

We are left with 5×5

∴5×5 i.e., 25 is to be divided.

Hence, least number to be divided for getting perfect cube = 25** Ans.**

**Que-5: Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.**

**Solution-**2560 = (2×2×2×2×2×2×2×2×2×5)

Making them in groups of 3 equal factors, we are left 5

∴ To make it into a group of 3, we have to multiply it by 5×5 i.e. by 25.

Hence, the smallest number by which it is multiplied = 25** Ans.**

**Que-6: Find the cube root of :**

**(i) 216/2197 (ii) 4*(508/1331) (iii) 42.875**

**Solution- **(i) On prime factorisation of the numbers individually, we get,

216 = 2×2×2×3×3×3 = 2³×3³ = 6³.

2197 = 13×13×13 = 13³.

Then,

3√216/2197 = 3√6³/13³ = 6/13. **Ans.**

(ii) 4*(508/1331) = 5832/1331

5832 = 18 x 18 x 18

1331 = 11 x 11 x 11

5832/1331 = 18*18 *18/11*11*11

= 18/11 = 1*(7/11) **Ans**.

(iii) 3√42.875 ≈ 3.5

**— : End of Squares and Cube Roots Class 8 RS Aggarwal Exe-3E Goyal Brothers ICSE Foundation Maths Solutions Ch-3 :–**

**Return to- ICSE Class -8 RS Aggarwal Goyal Brothers Math Solutions**

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