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
2). Linear Equations in One Variable
3). Understanding Quadrilaterals
4). Data Handling
5). Squares and Square Roots
6). Cubes and Cube Roots