Question

if a number is divided by the 4, the result is a perfect square but not a perfect cube. If the same number is divided by 27, the result is a perfect cube but not a perfect square. Find the smallest such number​

Answer 1

Answer:

46656

Step-by-step explanation:

Let the number= x

then as per question;

x/4= a² => x=4a²

x/27=b³ => x=27b³

4a²=27b³

a=3n, b=2m

4*(3n)²=27*(2m)³

4*9n²=27*8m³

n²=6m³ => minimum of m=6, n= 6²=36

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a=3n= 108

b=2m= 12

x=4a²= 4*108²= 46656

x=27b³= 27*12³= 46656

Answer: minimum number to satisfy the given condition is 46656