Cubes and Cube Roots - Solutions 2

CBSE Class –VIII Mathematics
NCERT Solutions
CHAPTER - 7
Cubes and Cube Roots (Ex. 7.2)

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

Ans. (i) 64

= 4

(ii) 512

= 8

(iii) 10648

= 22

(iv) 27000

= 30

(v) 15625

= 25

(vi) 13824

= 24

(vii) 110592

= 48

(viii) 46656

= 36

(ix) 175616

= 56

(x) 91125

= 45

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.

Ans. (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

= 1331
[Four digit number]

(vi) False Since

= 970299
[Six digit number]

(vii) True

= 1
[Single digit number]

= 8
[Single digit number]

3. You are told that 1,331 is a perfect cube. Can you guess without factorization what is its cube root? Similarly guess the cube roots of 4913, 12167, 32768.

Ans. We know that

= 1000 and Possible cube of

= 1331
Since, cube of unit’s digit

= 1
Therefore, cube root of 1331 is 11.

4913
We know that