# NCERT Solution for class 8 maths chapter 7-Cubes and Cube Roots

**NCERT solutions for class 8 maths** chapter 7 Cubes and Cube Roots is prepared by academic team of Physics Wallah. We have prepared solutions for all exercise of chapter 7. Given below is step by step solutions of all questions given in NCERT textbook for chapter 7. Read chapter 7 theory make sure you have gone through the theory part of chapter 7 from NCERT textbook and you have learned the formula of the given chapter. Physics Wallah prepared a detail notes and additional questions, **maths doubts** for class 8 maths with short notes of all **maths formula** of class 8 maths. Do read these contents before moving to solve the exercise of NCERT chapter 7

### NCERT Solutions for Class 8 Maths Exercise 7.1

**Question 1.**

Which of the following numbers are not perfect cubes:

(i)216

(ii)128

(iii)1000

(iv)100

(v)46656

**Solution :**

(i)216

Prime factors of 216 = 2×2×2×3×3×3

Here all factors are in groups of 3’s (in triplets)

Therefore, 216 is a perfect cube number.

(ii) 128

Prime factors of 128

= 2×2×2×2×2×2×2

Here one factor 2 does not appear in a 3’s group.

Therefore, 128 is not a perfect cube.

(iii) 1000

Prime factors of 1000 = 2×2×2×3×3×3

Here all factors appear in 3’s group.

Therefore, 1000 is a perfect cube.

(iv) 100

Prime factors of 100 = 2 x 2 x 5 x 5

Here all factors do not appear in 3’s group.

Therefore, 100 is not a perfect cube.

(v) 46656

Prime factors of 46656

= **2x2x2x2x2x2x3x3x3x3x3x3**

Here all factors appear in 3’s group.

Therefore, 46656 is a perfect cube.

**Question 2.** Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

(i)243

(ii)256

(iii)72

(iv)675

(v)100

**Solution :**

(i)243

Prime factors of 243 = **3x3x3x3x3**

Here 3 does not appear in 3’s group.

Therefore, 243 must be multiplied by 3 to make it a perfect cube.

(ii) 256

Prime factors of 256

= 2×2×2×2×2×2×2×2

Here one factor 2 is required to make a 3’s group.

Therefore, 256 must be multiplied by 2 to make it a perfect cube.

(iii) 72

Prime factors of 72 = 2×2×2×3×3

Here 3 does not appear in 3’s group.

Therefore, 72 must be multiplied by 3 to make it a perfect cube.

(iv) 675

Prime factors of 675 = 3 × 3 × 3 × 5 × 5

Here factor 5 does not appear in 3’s group.

Therefore 675 must be multiplied by 3 to make it a perfect cube.

(v) 100

Prime factors of 100 =2 × 2 × 5 × 5

Here factor 2 and 5 both do not appear in 3’s group.

Therefore 100 must be multiplied by = 10 to make it a perfect cube.

**Question 3.** Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:

(i)81

(ii)128

(iii)135

(iv)192

(v)704

**Solution :**

(i)81

Prime factors of 81 = 3 × 3 × 3 × 3

Here one factor 3 is not grouped in triplets.

Therefore 81 must be divided by 3 to make it a perfect cube.

(ii) 128

Prime factors of 128 =

Here one factor 2 does not appear in a 3’s group.

Therefore, 128 must be divided by 2 to make it a perfect cube.

(iii) 135

Prime factors of 135 =

Here one factor 5 does not appear in a triplet.

Therefore, 135 must be divided by 5 to make it a perfect cube.

(iv) 192

Prime factors of 192 =

Here one factor 3 does not appear in a triplet.

Therefore, 192 must be divided by 3 to make it a perfect cube.

(v) 704

Prime factors of 704

=

Here one factor 11 does not appear in a triplet.

Therefore, 704 must be divided by 11 to make it a perfect cube.

**Question 4.** Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

Ans. Given numbers =

Since, Factors of 5 and 2 both are not in group of three.

Therefore, the number must be multiplied by 2 × 5 × 2 = 20 to make it a perfect cube.

Hence he needs 20 cuboids.

### NCERT Solutions for Class 8 Maths Exercise 7.2

**Question 1.**

Find the cube root of each of the following numbers by prime factorization method:

(i) 64

(ii) 512

(iii) 10648

(iv) 27000

(v) 15625

(vi) 13824

(vii) 110592

(viii) 46656

(ix) 175616

(x) 91125

**Solution :** (i) 64

= 4

(ii) 512

(iii) 10648

(iv) 27000

(v) 15625

=5 × 5

= 25

(vi) 13824

=

= 24

(vii) 110592

= **2×2×2×2×3**

= 48

(viii) 46656

= 36

(ix) 175616

= 56

(x) 91125

**Question 2.**

State true or false:

(i) Cube of any odd number is even.

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

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

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

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

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

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

**Solution :** (i) False

Since, are all odd.

(ii) True

Since, a perfect cube ends with three zeroes. e.g. so on

(iii) False

Since,

(Did not end with 25)

(iv) False

Since = 1728

[Ends with 8]

And = 10648

[Ends with 8]

(v) False Since = 1000

[Four digit number]

And **11³ =** 1331

[Four digit number]

(vi) False Since **99³ **= 970299

[Six digit number]

(vii) True

**1³** = 1

[Single digit number]

** 2³** = 8

[Single digit number]

**Question 3.**

You are told that 1,331 is a perfect cube. Can you guess with factorization what is its cube root? Similarly guess the cube roots of 4913, 12167, 32768.

**Solution :**

We know that **10³ **= 1000 and Possible cube of **11³ **= 1331

Since, cube of unit’s digit **1³ ** = 1

Therefore, cube root of 1331 is 11.

4913

We know that 7**³ **= 343

Next number comes with 7 as unit place **17³ **= 4913

Hence, cube root of 4913 is 17.

12167

We know that **3³ **= 27

Here in cube, ones digit is 7

Now next number with 3 as ones digit

13**³ **= 2197

And next number with 3 as ones digit

23**³ ** = 12167

Hence cube root of 12167 is 23.

32768

We know that 2**³ **= 8

Here in cube, ones digit is 8

Now next number with 2 as ones digit

12**³ **= 1728

And next number with 2 as ones digit

22**³ **= 10648

And next number with 2 as ones digit

32**³ ** = 32768

Hence cube root of 32768 is 32.

### Notes,worksheet and solved question for Maths class 8

- class 8 maths notes on chapter Liner equation in one variable
- class 8 maths notes on chapter algebric expression
- class 8 maths notes on chapter Mensuration
- class 8 maths notes on chapter Square and square roots
- class 8 maths notes on chapter statistice
- class 8 maths notes on chapter practical Geometry
- class 8 maths notes on chapter commericial maths
- class 8 maths notes on chapter solid shape
- class 8 maths notes on chapter quadrilaterals
- class 8 maths notes on chapter exponents
- class 8 maths notes on chapter factorisation
- class 8 maths notes on chapter inverse proporation
- class 8 maths notes on chapter cube and cube roots

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