## 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 m^{3}.

Solution:

Volume of a cube = 4096 m^{3}

∴ Its side = \(\sqrt[3]{4096}\) m