Cubes And Cube Roots  

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

64 = 2 X 2 X 2 X 2 X 2 X 2

64 = 2 X 2 X 2 X 2 X 2 X 2

64 = 2³ X 2³

³√64 = ³√2³ X 2³

       = 2 X 2

       = 4

Ans: ³√64 = 4

(ii) 512

512 = 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2

512 = 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2

512 = 2³ X 2³ X 2³

³√512 = ³√2³ X 2³ X 2³

       = 2 X 2 X 2

       = 8

Ans: ³√512 = 8

(iii) 10648

 

10648 = 2 X 2 X 2 X 11 X 11 X 11

10648 = 2 X 2 X 2 X 11 X 11 X 11

10648 = 2³ X 11³

³√10648 = ³√2³ X 11³

       = 2 X 11

       = 22

Ans: ³√10648= 22

(iv) 27000

27000= 2 X 2 X 2 X 3 X 3 X 3 X 5 X 5 X 5

27000= 2 X 2 X 2 X 3 X 3 X 3 X 5 X 5 X 5

27000= 2³ X 3³ X 5³

³√27000 = ³√2³ X 3³ X 5³

       = 2 X 3 X 5

       = 30

Ans: ³√27000 = 30

(v) 15625

15625= 5 X 5 X 5 X 5 X 5 X 5

15625= 5 X 5 X 5 X 5 X 5 X 5

15625= 5³ X 5³

³√15625 = ³√5³ X 5³

       = 5 X 5

       = 25

Ans: ³√15625 = 25

(vi) 13824

13824= 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 3 X 3 X 3

13824= 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 3 X 3 X 3

13824= 2³ X 2³ X 2³ X 3³

³√13824 = ³√2³ X 2³ X 2³ X 3³

       = 2 X 2 X 2 X 3

       = 24

Ans: ³√13824 = 24

(vii) 110592

110592= 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2X 3 X 3 X 3

110592= 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2X 3 X 3 X 3

110592= 2³ X 2³ X 2³ X 2³ X 3³

³√110592 = ³√2³ X 2³ X 2³ X 2³ X 3³

       = 2 X 2 X 2 X 2 X 3

       = 48

Ans: ³√110592 = 48

(viii) 46656

46656= 2 X 2 X 2 X 2 X 2 X 2 X 3 X 3 X 3 X 3 X 3 X 3

46656= 2 X 2 X 2 X 2 X 2 X 2 X 3 X 3 X 3 X 3 X 3 X 3

46656= 2³ X 2³ X 3³ X 3³

³√46656 = ³√2³ X 2³ X 3³ X 3³

       = 2 X 2 X 3 X 3

       = 36

Ans: ³√46656 = 36

(ix) 175616

175616= 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 7 X 7 X 7

175616= 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 7 X 7 X 7

175616= 2³ X 2³ X 2³ X 7³

³√175616 = ³√2³ X 2³ X 2³ X 7³

       = 2 X 2 X 2 X 7

       = 56

Ans: ³√175616 = 56

(x) 91125

91125= 3 X 3 X 3 X 3 X 3 X 3 X 5 X 5 X 5

91125= 3 X 3 X 3 X 3 X 3 X 3 X 5 X 5 X 5

91125= 3³ X 3³ X 5³

³√91125 = ³√3³ X 3³ X 5³

       = 3 X 3 X 5

       = 45

Ans: ³√91125 = 45

2). State true or false.

i). Cube of any odd number is even.

Ans: False

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

Ans: True

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

Ans: True

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

Ans: False

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

Ans: False

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

Ans: False

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

Ans: False

Click here for the solutions of Std 8 Maths

1). Rational Numbers

 Exercise 1.1

2). Linear Equations in One Variable

Exercise 2.1

Exercise 2.2

3). Understanding Quadrilaterals

Exercise 3.1

Exercise 3.2

Exercise 3.3

Exercise 3.4

4). Data Handling

Exercise 4.1

Exercise 4.2

5). Squares and Square Roots

Exercise 5.1

Exercise 5.2

Exercise 5.3

Exercise 5.4

6). Cubes and Cube Roots

Exercise 6.1

Exercise 6.2