Students can refer to and download RD Sharma Solutions for Class 8 Maths from the links provided below. In Exercise 4.2 of RD Sharma Solutions Class 8 Maths Chapter 4 Cubes and Cube Roots, we will discuss problems based on cubes of negative integers and cubes of rational numbers. RD Sharma Class 8 Solutions are customised and designed in a step-by-step manner by our expert team, which helps students in gaining proficiency in the concepts.
RD Sharma Solutions for Class 8 Maths Exercise 4.2 Chapter 4 Cubes and Cube Roots
Access Answers to RD Sharma Solutions for Class 8 Maths Exercise 4.2 Chapter 4 Cubes and Cube Roots
1. Find the cubes of:
(i) -11
(ii) -12
(iii) -21
Solution:
(i) -11
The cube of 11 is
(-11)3 = -11× -11× -11 = -1331
(ii) -12
The cube of 12 is
(-12)3 = -12× -12× -12 = -1728
(iii) -21
The cube of 21 is
(-21)3 = -21× -21× -21 = -9261
2. Which of the following integers are cubes of negative integers?
(i) -64
(ii) -1056
(iii) -2197
(iv) -2744
(v) -42875
Solution:
(i) -64
The prime factors of 64 are
64 = 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23
= 43
∴ 64 is a perfect cube of negative integer – 4.
(ii) -1056
The prime factors of 1056 are
1056 = 2 × 2 × 2 × 2 × 2 × 3 × 11
1056 is not a perfect cube.
∴ -1056 is not a cube of negative integer.
(iii) -2197
The prime factors of 2197 are
2197 = 13 × 13 × 13
= 133
∴ 2197 is a perfect cube of negative integer –13.
(iv) -2744
The prime factors of 2744 are
2744 = 2 × 2 × 2 × 7 × 7 × 7
= 23 × 73
= 143
2744 is a perfect cube.
∴ -2744 is a cube of negative integer – 14.
(v) -42875
The prime factors of 42875 are
42875 = 5 × 5 × 5 × 7 × 7 × 7
= 53 × 73
= 353
42875 is a perfect cube.
∴ -42875 is a cube of negative integer – 35.
3. Show that the following integers are cubes of negative integers. Also, find the integer whose cube is the given integer.
(i) -5832
(ii) -2744000
Solution:
(i) -5832
The prime factors of 5832 are
5823 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
= 23 × 33 × 33
= 183
5832 is a perfect cube.
∴ -5832 is a cube of negative integer – 18.
(ii) -2744000
The prime factors of 2744000 are
2744000 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 × 7 × 7 × 7
= 23 × 23× 53 × 73
2744000 is a perfect cube.
∴ -2744000 is a cube of negative integer – 140.
4. Find the cube of:
(i) 7/9 (ii) -8/11
(iii) 12/7 (iv) -13/8
(v)
(ix) 0.08 (x) 2.1
Solution:
(i) 7/9
The cube of 7/9 is
(7/9)3 = 73/93 = 343/729
(ii) -8/11
The cube of -8/11 is
(-8/11)3 = -83/113 = -512/1331
(iii) 12/7
The cube of 12/7 is
(12/7)3 = 123/73 = 1728/343
(iv) -13/8
The cube of -13/8 is
(-13/8)3 = -133/83 = -2197/512
(v)
The cube of 12/5 is
(12/5)3 = 123/53 = 1728/125
(vi)
The cube of 13/4 is
(13/4)3 = 133/43 = 2197/64
(vii) 0.3
The cube of 0.3 is
(0.3)3 = 0.3×0.3×0.3 = 0.027
(viii) 1.5
The cube of 1.5 is
(1.5)3 = 1.5×1.5×1.5 = 3.375
(ix) 0.08
The cube of 0.08 is
(0.08)3 = 0.08×0.08×0.08 = 0.000512
(x) 2.1
The cube of 2.1 is
(2.1)3 = 2.1×2.1×2.1 = 9.261
5. Find which of the following numbers are cubes of rational numbers:
(i) 27/64
(ii) 125/128
(iii) 0.001331
(iv) 0.04
Solution:
(i) 27/64
We have,
27/64 = (3×3×3)/ (4×4×4) = 33/43 = (3/4)3
∴ 27/64 is a cube of 3/4.
(ii) 125/128
We have,
125/128 = (5×5×5)/ (2×2×2×2×2×2×2) = 53/ (23×23×2)
∴ 125/128 is not a perfect cube.
(iii) 0.001331
We have,
1331/1000000 = (11×11×11)/ (100×100×100) = 113/1003 = (11/100)3
∴ 0.001331 is a perfect cube of 11/100
(iv) 0.04
We have,
4/10 = (2×2)/(2×5) = 22/(2×5)
∴ 0.04 is not a perfect cube.
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