NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.2

NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.2

 

Introduction :

In this exercise/article we will learn about cubes and cube roots. Cube is 3d picture of square and you will find the cubes root of a cube number in this exercise and find cube and cube roots through prime factorisation method . The symbol is cube root \(\displaystyle \sqrt[3]{{}}\) .

 

NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots :

Class 8 Maths Exercise 7.2 (Page-116)

Q1. Find the cube root of each of the following numbers by the prime factorisation method.

(i) 64

Solution :

Given, 64

= \(\displaystyle \sqrt[3]{{64}}\)

= \(\displaystyle \sqrt[3]{{2\times 2\times 2\times 2\times 2\times 2}}\)

= \(\displaystyle \sqrt[3]{{{{2}^{3}}\times {{2}^{3}}}}\)

= 2 × 2

= 4

Hence, the cube root of 64 = 4

(ii) 512

Solution :

Given, 512

= \(\displaystyle \sqrt[3]{{512}}\)

= \(\displaystyle \sqrt[3]{{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}}\)

= \(\displaystyle \sqrt[3]{{{{2}^{3}}\times {{2}^{3}}\times {{2}^{3}}}}\)

= 2 × 2 × 2

= 8

Hence, the cube root of 512 = 8

(iii) 10648

Solution :

Given, 10648

= \(\displaystyle \sqrt[3]{{10648}}\)

= \(\displaystyle \sqrt[3]{{2\times 2\times 2\times 11\times 11\times 11}}\)

= \(\displaystyle \sqrt[3]{{{{2}^{3}}\times {{{11}}^{3}}}}\)

= 2 × 11

= 22

Hence, the cube root of 10648 = 22

(iv) 27000

Solution :

Given, 27000

= \(\displaystyle \sqrt[3]{{27000}}\)

= \(\displaystyle \sqrt[3]{{2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 5}}\)

= \(\displaystyle \sqrt[3]{{{{2}^{3}}\times {{3}^{3}}\times {{5}^{3}}}}\)

= 2 × 3 × 5

= 30

Hence, the cube root of 27000 = 30

(v) 15625

Solution :

Given, 15625

= \(\displaystyle \sqrt[3]{{15625}}\)

= \(\displaystyle \sqrt[3]{{5\times 5\times 5\times 5\times 5\times 5}}\)

= \(\displaystyle \sqrt[3]{{{{5}^{3}}\times {{5}^{3}}}}\)

= 5 × 5

= 25

Hence, the cube root of 15625 = 25

(vi) 13824

Solution :

Given, 13824

= \(\displaystyle \sqrt[3]{{13824}}\)

= \(\displaystyle \sqrt[3]{{2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,3\,\times \,3\,\times \,3}}\,\)

= \(\displaystyle \sqrt{{{{2}^{3}}\,\times \,{{2}^{3}}\,\times {{2}^{3}}\,\times {{3}^{3}}}}\)

= 2 × 2 × 2 × 3

= 24

Hence, the cube root of 13824 = 24

(vii) 110592

Solution :

Given, 110592

= \(\displaystyle \sqrt[3]{{110592}}\)

= \(\displaystyle \sqrt[3]{{2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,2\,\times \,3\,\times \,3\,\times \,3}}\,\)

= \(\displaystyle \sqrt{{{{2}^{3}}\,\times \,{{2}^{3}}\,\times {{2}^{3}}\,\times {{2}^{3}}\,\times {{3}^{3}}}}\)

= 2 × 2 × 2 × 2 × 3

= 48

Hence, the cube root of 110592 = 48

(viii) 46656

Solution :

Given, 46656

 

NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots :

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