(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 \(1000 = 2\times2\times2\times5\times5\times5\)
Here all factors appear in \(3\)’s group.
Therefore, \(1000\) is a perfect cube.
(iv) \(100\)
Prime factors of \( 100 = 2 \times 2 \times 5 \times 5\)
Here all factors do not appear in \(3\)’s group.
Therefore, \(100\) is not a perfect cube.
(v) \(46656\)
Prime factors of \(46656 =2 \times2\times2\times2\times2\times2\times3\times3\times3\times3\times3\times3\)
Here all factors appear in \(3\)’s group.
Therefore, \(46656\) is a perfect cube.
Colours | Number of people |
---|---|
Blue | 18 |
Green | 9 |
Red | 6 |
Yellow | 3 |
Total | 36 |
Mention the following.
(i) Two examples of social practices prevailing then.
(ii) Two oppressive policies of the British.
(iii) Two ways in which common people suffered.
(iv) Four reasons for the discontent that led to the 1857 War of Independence.