Question

(c) Find the smallest positive integer k such that 360 k is a cube number.

Answer 1

Answer:

75

Step-by-step explanation:

k=75

Answer 2

The smallest positive integer value of k will be 75.

Given:

a number 360k, where k is a positive integer

To Find:

value of k for which 360k is a cube number

Solution:

360k can be written as-

360k = 3² × 5 × 2³ × k

Now, for 360k to be a cube number, we need one more 3 and 2 more fives. We already have 3 twos.

thus, we need to multiply 360 by at least 75 in order to make it a cube.

360 × 75 = 27000, which is the cube of 30.

Thus, the smallest positive integer value of k will be 75.

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