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 :

Making factors of 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2^{6} = (2^{2})^{3} = 4^{3}

Hence, it’s a perfect cube.

Factors of 216 = 2 × 2 × 2 × 3 × 3 × 3 = 2^{3} × 3^{3} = 6^{3}

Hence, it’s a perfect cube.

Factors of 243 = 3 × 3 × 3 × 3 × 3 = 3^{5} = 3^{3} × 3^{2}

Hence, it’s not a perfect cube.

Factors of 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 2^{3} × 5^{3} = 10^{3}

Hence, it’s a perfect cube.

Factors of 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2^{6} × 3^{3} = (4 × 3 )^{3} = 12^{3}

Hence, it’s a perfect cube.

Factors of 3087 = 3 × 3 × 7 × 7 × 7 = 3^{2} × 7^{3}

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 = 5^{3} × 11^{3} = 55^{3}

Hence, it’s a perfect cube.

Factors of 456533 = 11 × 11 × 11 × 7 × 7 × 7 = 11^{3} × 7^{3} = 77^{3}

Hence, it’s a perfect cube.

Rate this question :

Which of the following numbers are not perfect cubes?

(i) 64

(ii) 216

(iii) 243

(iv) 1728

RD Sharma - MathematicsFind the cubes of the following numbers by column method:

(i) 35

(ii) 56

(iii) 72

RD Sharma - Mathematics