ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2

Question 1.
Find the cube root of each of the following numbers by prime factorisation:
(i) 12167
(ii) 35937
(iii) 42875
(iv) 21952
(v) 373248
(vi) 32768
(vii) 262144
(viii) 157464
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q1.1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q1.2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q1.3
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q1.4
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q1.5
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q1.6
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q1.7

Question 2.
Find the cube root of each of the following cube numbers through estimation.
(i) 19683
(ii) 59319
(iii) 85184
(iv) 148877
Solution:
(i) 19683
Grouping in 3’s from right to left, 19,683
In the first group 683, the unit digit is 3
∴ The cube root will be 7
and in the second group, 19
Cubing 23 = 8 and 33 = 27
∴ 8 < 14 < 21
∴ The tens digit of the cube will be 2
∴ Cube root of 19683 = 27

(ii) 59319
Grouping in 3’s, from right to left. 59,319
In first group, 319 unit digit is 9
∴ Unit digit of its cube root will be 9
and group 2nd, 59
33 = 27, 43 = 64
27 < 59 < 64
∴ Ten’s digit will be 3
∴ Cube root = 39

(iii) 85184
Grouping in 3’s from right to left 85,184
In group first 184, the unit digit is 4
∴ Unit digit of its cube root will be 4 and in group 2nd 85,
43 = 64 and 53 = 125
64 < 85 < 125
∴ Ten’s digit of cube root will be 4
∴ Cube root = 44

(iv) 148877
Grouping in 3’s, from right to left 148,877
In the first group 877, unit digit is 7
∴ The unit digit of cube root will be 3
and in group 2nd 148
53 = 125, 63 = 216
125 < 148 < 216
∴ Ten’s digit of cube root will be 5
∴ Cube root = 53

Question 3.
Find the cube root of each of the following numbers:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q3.1
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 0
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q3.2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q3.3
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q3.4

Question 4.
Evaluate the following:
(i) \(\sqrt[3]{512 \times 729}\)
(ii) \(\sqrt[3]{(-1331) \times(3375)}\)
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q4.1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q4.2

Question 5.
Find the cube root of the following decimal numbers:
(i) 0.003375
(ii) 19.683
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q5.1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q5.2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q5.3

Question 6.
Evaluate: \(\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}\)
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q6.1

Question 7.
Multiply 6561 by the smallest number so that product is a perfect cube. Also, find the cube root of the product.
Solution:
6561
Factorising, we get
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q7.1
6561 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3
Grouping of the equal factors in 3’s,
we see that 3 × 3 is left ungrouped in 3’s.
In order to complete it in triplet, we should multiply it by 3.
Hence, required smallest number = 3
and cube root of the product = 3 × 3 × 3 = 27

Question 8.
Divide the number 8748 by the smallest number so that the quotient is a perfect cube. Also, find the cube root of the quotient.
Solution:
8748
Factorising, we get
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q8.1
8748 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
Grouping of the equal factor in 3’s
we get that 2 × 2 × 3 is left without grouping.
So, dividing 8748 by 12, we get 729
whose cube root is 3 × 3 = 9

Question 9.
The volume of a cubical box is 21952 m3. Find the length of the side of the box.
Solution:
The volume of a cubical box 21952 m2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Q9.1
= \(\sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7} \mathrm{m}\)
= 2 × 2 × 7 = 28 m

Question 10.
Three numbers are in the ratio 3 : 4 : 5. If their product is 480, find the numbers.
Solution:
Three numbers are in the ratio 3:4:5
and their product = 480
Let numbers be 3x, Ax, 5x, then
3x × 4x × 5x = 480 ⇒ 60 × 3 = 480
⇒ x3 = \(\frac{480}{60}\) = 8 = (2)3
∴ x = 2
∴ Number are 2 × 3, 2 × 4, 2 × 5
= 6, 8 and 10

Question 11.
Tw’o numbers are in the ratio 4 : 5. If difference of their cubes is 61, find the numbers.
Solution:
Two numbers are in the ratio = 4 : 5
Difference between their cubes = 61
Let the numbers be 4x, 5x
∴ (5x)3 – (4x)3 = 61
125x3 – 64x3 = 61 ⇒ 61x3 = 61
⇒ x3 = 1 = (1)3
∴ x = 1
∴ Numbers are 4x = 4 × 1 = 4 and 5 × 1 = 5
Hence numbers are = 4, 5

Question 12.
Difference of two perfect cubes is 387. If the cube root of the greater of two numbers is 8, find the cube root of the smaller number.
Solution:
Difference in two cubes = 387
Cube root of the greater number = 8
∴ Greater number = (8)3 = 8 × 8 × 8 = 512
Hence, second number = 512 – 387 = 125
and cube root of 125 = \(\sqrt[3]{125}\)
= \(\sqrt[3]{5 \times 5 \times 5}\) = 5

ML Aggarwal Class 8 Solutions for ICSE Maths

Leave a Reply

Your email address will not be published. Required fields are marked *