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

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 :–