Q. 84.8( 6 Votes )

# 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

Answer :

(i) 64

Making factors of 64 = 2 × 2 × 2 × 2 × 2 × 2 = 26 = (22)3 = 43

Hence, it’s a perfect cube.

(ii) 216

Factors of 216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33 = 63

Hence, it’s a perfect cube.

(iii) 243

Factors of 243 = 3 × 3 × 3 × 3 × 3 = 35 = 33 × 32

Hence, it’s not a perfect cube.

(iv) 1000

Factors of 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 23 × 53 = 103

Hence, it’s a perfect cube.

(v) 1728

Factors of 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 26 × 33 = (4 × 3 )3 = 123

Hence, it’s a perfect cube.

(vi) 3087

Factors of 3087 = 3 × 3 × 7 × 7 × 7 = 32 × 73

Hence, it’s not a perfect cube.

(vii) 4608

Factors of 4608 = 2 × 2 × 3 × 113

Hence, it’s not a perfect cube.

(viii) 106480

Factors of 106480 = 2 × 2 × 2 × 2 × 5 × 11 × 11 × 11

Hence, it’s not a perfect cube.

(ix) 166375

Factors of 166375 = 5 × 5 × 5 × 11 × 11 × 11 = 53 × 113 = 553

Hence, it’s a perfect cube.

(x) 456533

Factors of 456533 = 11 × 11 × 11 × 7 × 7 × 7 = 113 × 73 = 773

Hence, it’s a perfect cube.

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