Latest Updated : October 2023

If you are in search of **NCERT solutions for Class 8 Maths Chapter** **6 Cube and Cube Roots**, then you are at the right place. When it comes to **Mathematics**, it is a subject that holds value for students across various academic streams, be it science, biology, or commerce and having a very good understanding of basic math concepts will help you in achieving your goal and make it much more easier.

Here we provide detailed **NCERT solutions for Class 8 Maths** of all the chapters, **exercise wise** with **updated syllabus by NCERT**. These NCERT solutions for Class 8 Maths have been carefully crafted to provide detailed explanations, ensuring that students can grasp the concepts effectively. We also provide extra practice questions for the same, so feel free to bookmark **ncertforclass8.com** to boost your preparation.

## NCERT Solutions for Class 8 Maths Chapter **6 Cube and Cube Roots**

Ex 6.2

**Class 8 Maths Chapter** **6 Cube and Cube Roots** **Exercise 6.**2

**Exercise 6.2**

**1. Find the cube root of each of the following numbers by prime factorisation method.(i) 64 (ii) 512 (iii) 10648 (iv) 27000(v) 15625 (vi) 13824 (vii) 110592 (viii) 46656(ix) 175616 (x) 91125**

Solution:

**(i) 64**

`\[_3\sqrt{64}=_3\sqrt{2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2}\ \ \]`

`\[_3\sqrt{64}=\ 2\ x\ 2\ =\ 4\]`

**(ii) 512**

`\[_3\sqrt{512}=\ _3\sqrt{2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2}\]`

`\[_3\sqrt{512}=2\ x\ 2\ x\ 2\ =\ 8\]`

**(iii) 10648**

`\[_3\sqrt{10648}=_3\sqrt{2\ x\ 2\ x\ 2\ x\ 11\ x\ 11\ x\ 11}\]`

`\[_3\sqrt{10648}=2\ x\ 11\ =\ 22\]`

**(iv) 27000**

`\[_3\sqrt{27000}=\ _3\sqrt{2\ x\ 2\ x\ 2\ x\ 3\ x\ 3\ x\ 3\ x\ 5\ x\ 5\ x\ 5}\]`

`\[_3\sqrt{27000}=\ 2\ x\ 3\ x\ 5=30\]`

**(v) 15625 **

`\[_3\sqrt{15625\ }=\ _3\sqrt{5\ x\ 5\ x\ 5\ x\ 5\ x\ 5\ x\ 5}\]`

`\[_3\sqrt{15625}=\ 5\ x\ 5\ =\ 25\]`

**(vi) 13824 **

`\[_3\sqrt{13824\ }=_3\sqrt{2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 3\ x\ 3\ x\ 3\ }\]`

`\[_3\sqrt{13824\ }=2\ x\ 2\ x\ 2\ x\ 3\ =\ 24\]`

**(vii) 110592 **

`\[_3\sqrt{110592\ }=\ _3\sqrt{2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 3\ x\ 3\ x\ 3}\]`

`\[_3\sqrt{110592\ }=\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 3\ =\ 48\]`

**(viii) 46656**

`\[_3\sqrt{46656\ }=\ _3\sqrt{2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 3\ x\ 3\ x\ 3\ x\ 3\ x\ 3\ x\ 3}\]`

`\[_3\sqrt{46656\ }=\ 2\ x\ 2\ x\ 3\ x\ 3\ =\ 36\]`

**(ix) 175616 **

`\[_3\sqrt{175616\ }=_{\ 3}\sqrt{2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 2\ x\ 7\ x\ 7\ x\ 7}\]`

`\[_3\sqrt{175616\ }=2\ x\ 2\ x\ 2\ x\ 7\ =\ 56\]`

**(x) 91125**

`\[_3\sqrt{91125\ }=_3\sqrt{3\ x\ 3\ x\ 3\ x\ 3\ x\ 3\ x\ 3\ x\ 5\ x\ 5\ x\ 5}\]`

`\[_3\sqrt{91125\ }=3\ x\ 3\ x\ 5\ =\ 45\]`

**2. State true or false.**

Solution:

**(i) Cube of any odd number is even.**

(i) False

`\[Since\ 1^3=1,\ 3^3=27,\ 5^3=125\ ...\ etc\ are\ all\ odd.\ ∴\ Cube\ of\ any\ odd\ number\ will\ always\ be\ odd.\]`

**(ii) A perfect cube does not end with two zeros.**

(ii) True

Since, a perfect cube ends with three zeroes.

`\[10^3=\ 1000,\ 200^3=\ 8000000,\ 1000^3=1000000000....\ so\ on.\]`

**(iii) If square of a number ends with 5, then its cube ends with 25.**

(iii) False

`\[Since,\ 5^2=\ 25,\ 5^3=\ 125,\ 15^2=225,\ 15^3=\ 3375\ \ \ it\ does\ not\ end\ with\ 25.\]`

**(iv) There is no perfect cube which ends with 8.**

(iv) False

`\[2^3=\ 8\ \left[Ends\ with\ 8\right]\]`

`\[12\ ^3=\ 1728\ \ \left[Ends\ with\ 8\right]\]`

`\[22\ ^3=\ 10648\ \left[Ends\ with\ 8\right]\]`

**(v) The cube of a two digit number may be a three digit number.**

(v) False

`\[10^3=\ 1000\ \left[Four\ digit\ number\right]\]`

`\[11^3=\ 1331\ \left[Four\ digit\ number\right]\]`

**(vi) The cube of a two digit number may have seven or more digits.**

(vi) False

`\[99^3=\ 970299\ \left[six\ digit\ number\ can\ be\ \max imum\right]\]`

**(vii) The cube of a single digit number may be a single digit number**

(vii) True

`\[1^3=\ 1\ \ \]`

`\[2^3=\ 8\]`

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