(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.
Fill in the blanks using the correct form of the verbs in brackets.
My little sister is very naughty. When she ____ (come) back from school yesterday, she had _____(tear) her dress. We _____(ask) her how it had _____(happen). She ______(say) she _____ _____ (have, quarrel) with a boy. She _____ _____ (have, beat) him in a race and he _____ ____ (have, try) to push her. She _____ ____ (have, tell) the teacher and so he _____ _____ (have, chase) her, and she _____ _____ (have, fall) down and _____ _____ (have, tear) her dress.