Question

Q8) Find the smallest positive integer k) such that 360k is a cube number (perfect cube)​

Answer 1

Answer:

k = 75

Step-by-step explanation:

360

∧

36 10

∧ ∧

6 6 2 5

∧ ∧

2 3 2 3

Prime factorization of 360 is: 2³ · 3² · 5

Since we want a perfect cube, every number must be to the power of 3.

That means we need a 3 and 2 more 5s to make a cube

k = 3 × 5 × 5

=75

Answer 2

Answer:

k = 75

Step-by-step explanation:

360

∧

36 10

∧ ∧

6 6 2 5

∧ ∧

2 3 2 3

Prime factorization of 360 is: 2³ · 3² · 5

Since we want a perfect cube, every number must be to the power of 3.

That means we need a 3 and 2 more 5s to make a cube

k = 3 × 5 × 5

=75