Question

If 72 k is a perfect cube, find the smallest value of K.​

Answer 1

Answer:

k=3

Step-by-step explanation:

72k=x^3

72=2x2x2x3x3.

hence when 72 is multiplied by 3 it will become a perfect cube of 6.

therefore the value of k is 3

Answer 2

Answer:

72K=x

3

Let us prime factorize 72 .

72=2×2×2×3×3

For a number to be a perfect cube , it must have all the numbers in triplet.

Here , 3 is not in the form of triplet, hence we multiply (i) both the sides with 3.

⇒72×3=2×2×2×3×3×3

⇒216=2×2×2×3×3×3

Now 2 and 3 are in triplets.

⇒72K=216

⇒K= 72/216

⇒K=3