Question

Which of the following are the cubes of even numbers?

i. 216
ii. 729
iii. 512
iv. 3375
v. 1000

Answer 1

we know by the rule of even numbers the cubes of even numbers are always even.

So we look for the even numbers in the given set of numbers

216, 512, 1000 are the even numbers

Now we find the prime factors for 216, 512, 1000

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

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2³ × 2³ × 2³ = 8³

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

∴ 216, 512, 1000 are cubes of even numbers.