SOLUTION: im a real number,thrice of me gives you a perfect cube while the square root of mine gives you a prime number.who am i?

Question 869814: im a real number,thrice of me gives you a perfect cube while the square root of mine gives you a prime number.who am i?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let x = the number
Then 3x = a^3 where a = the base of the perfect cube
We can write x in terms of a:
x = a^3/3
The square root of x has to be a prime number:
sqrt(a^3/3) = prime
For the square root to be a whole number, a^3 must be divisible by 3, i.e. a=3,6,9 etc.
Try a=3 -> sqrt(27/3) = sqrt(9) = 3, which is prime
So x = 3^3/3 = 9
Ans: 9

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