Which of the following integers are cubes of negative integers ?(i) -6

1.	Which of the following integers are cubes of negative integers ?(i) -64(ii) -1056(iii) -2197
Answer» (i) -64 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2³ × 2³ = 4³ ∴ 64 is a perfect cube of negative integer – 4. (ii) -1056 1056 = 2 × 2 × 2 × 2 × 2 × 3 × 11 1056 is not a perfect cube. ∴ -1056 is not a cube of negative integer. (iii) -2197 2197 = 13 × 13 × 13 = 13³ ∴ 2197 is a perfect cube of negative integer – 13.

Which of the following integers are cubes of negative integers ?(i) -64(ii) -1056(iii) -2197

Answer»

(i) -64

64 = 2 × 2 × 2 × 2 × 2 × 2

= 2³ × 2³

= 4³

∴ 64 is a perfect cube of negative integer – 4.

(ii) -1056

1056 = 2 × 2 × 2 × 2 × 2 × 3 × 11

1056 is not a perfect cube.

∴ -1056 is not a cube of negative integer.

(iii) -2197

2197 = 13 × 13 × 13

= 13³

∴ 2197 is a perfect cube of negative integer – 13.