Which of the following are perfect cubes?
(i) 64 (ii) 216
(iii) 243 (iv) 1000
(v) 1728 (vi) 3087
(vii) 4608 (viii) 106480
(ix) 166375 (x) 456533
Making factors of 64 = 2 × 2 × 2 × 2 × 2 × 2 = 26 = (22)3 = 43
Hence, it’s a perfect cube.
Factors of 216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33 = 63
Hence, it’s a perfect cube.
Factors of 243 = 3 × 3 × 3 × 3 × 3 = 35 = 33 × 32
Hence, it’s not a perfect cube.
Factors of 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 23 × 53 = 103
Hence, it’s a perfect cube.
Factors of 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 26 × 33 = (4 × 3 )3 = 123
Hence, it’s a perfect cube.
Factors of 3087 = 3 × 3 × 7 × 7 × 7 = 32 × 73
Hence, it’s not a perfect cube.
Factors of 4608 = 2 × 2 × 3 × 113
Hence, it’s not a perfect cube.
Factors of 106480 = 2 × 2 × 2 × 2 × 5 × 11 × 11 × 11
Hence, it’s not a perfect cube.
Factors of 166375 = 5 × 5 × 5 × 11 × 11 × 11 = 53 × 113 = 553
Hence, it’s a perfect cube.
Factors of 456533 = 11 × 11 × 11 × 7 × 7 × 7 = 113 × 73 = 773
Hence, it’s a perfect cube.