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 :–
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