Question

Find the cube roots of the following numbers:
(1) −729
(2) 8000
(3) 2744
(4) 6859

Answer 1

(1) Cube root of −729 can be calculated by finding the cube root of 729.
729 = 3 × 3 × 3 × 3 × 3 × 3
= (3 × 3 × 3) × (3 × 3 × 3)
∴ $\sqrt[3]{729}$ = 3 × 3
= 9
∴ $\sqrt[3]{-729}$ = −9

(2) Prime factors of 8000 can be written as:
8000= 2×2×2×2×2×2×5×5×5
=(2×2×2) ×(2×2×2) ×(5×5×5)
∴ $\sqrt[3]{8000}$ = 2×2×5
∴ $\sqrt[3]{8000}$ = 20

(3) Prime factors of 2744 can be written as:
2744 = 2×2×2×7×7×7
= (2×2×2) ×(7×7×7)
∴ $\sqrt[3]{2744}$ = 2×7
∴ $\sqrt[3]{2744}$ = 14

(4) Prime factors of 6859 can be written as:
6859 = 19 × 361
=19 × 19 × 19
∴ $\sqrt[3]{6859}$ = 19