Question

 If 72K is a perfect cube, then what is the value of K. 

a) 1

(b) 2

(c) 9

(d) 4​

Answer 1

Answer:

Correct option is c

Given : 72K=x

Let us prime factorize 72 .

72=2×2×2×3×3..(i)

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= 216/72

⇒K=3

The value of K is 3