ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Check Your Progress
Question 1.
Show that each of the following numbers is a perfect cube. Also find the number whose cube is the given number:
(i) 74088
(ii) 15625
Solution:
(i) 74088
= 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7
Grouping the same kind of prime factors in 3’s,
we see that no factor has been left ungrouped.
So, 74088 is a perfect cube and its cube root is 2 × 3 × 7 = 42
(ii) 15625
= 5 × 5 × 5 × 5 × 5 × 5
Grouping the same kind of prime factors
we see that no factor is left ungrouped.
So, 15625 is a perfect cube and its cube root is 5 × 5 = 25.
Question 2.
Find the cube of the following numbers:
(i)-17
(ii) \(-3 \frac{4}{9}\)
Solution:
(i) Cube of-17 = (-17) × (-17) × (-17)
= -4913
(ii) Cube of \(-3 \frac{4}{9}=-\frac{31}{9}\)
= \(-\frac{31}{9} \times-\frac{31}{9} \times-\frac{31}{9}=-\frac{29791}{729}\)
= \(-40 \frac{631}{729}\)
Question 3.
Find the cube root of each of the following numbers by prime factorisation:
(i) 59319
(ii) 21952
Solution:
Question 4.
Find the cube root of each of the following numbers:
(i) -9261
(ii) \(2 \frac{43}{343}\)
(iii) 0.216
Solution:
Question 5.
Find the smallest number by which 5184 should be multiplied so that product is a perfect cube. Also find the cube root of the product.
Solution:
Factorising 5184
= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
Grouping the same kind of prime factors is 3’s,
we see that one factor 3 is left ungroup.
So, to complete it in 3’s, we must multiply 3 × 3 = 9.
Required least number = 9
and cube root of 5184 × 9 = 46656
= 2 × 2 × 3 × 3 = 36
Question 6.
Find the smallest number by which 8788 should be divided so that quotient is a perfect cube. Also, find the cube root of the quotient.
Solution:
Factorising 8788
= 2 × 2 × 13 × 13 × 13
Grouping of the same kind of factors,
we see that 2 × 2 has been left ungrouping.
So, 2 × 2 = 4 is the least number to divide it
∴ 8788 ÷ 4 = 2197 and its cube root = 13
Question 7.
Find the side of a cube whose volume is 4096 m3.
Solution:
Volume of a cube = 4096 m3
∴ Its side = \(\sqrt[3]{4096}\) m
