### 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  = 343
Next number comes with 7 as unit place  = 4913
Hence, cube root of 4913 is 17.
12167
We know that  = 27
Here in cube, ones digit is 7
Now next number with 3 as ones digit
= 2197
And next number with 3 as ones digit
= 12167
Hence cube root of 12167 is 23.
32768
We know that  = 8
Here in cube, ones digit is 8
Now next number with 2 as ones digit
= 1728
And next number with 2 as ones digit
= 10648
And next number with 2 as ones digit
= 32768
Hence cube root of 32768 is 32.