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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