document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #524472 by htmentor(1343) $\"\"$ $\"About$

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Let x = the number
\n" ); document.write( "Then 3x = a^3 where a = the base of the perfect cube
\n" ); document.write( "We can write x in terms of a:
\n" ); document.write( "x = a^3/3
\n" ); document.write( "The square root of x has to be a prime number:
\n" ); document.write( "sqrt(a^3/3) = prime
\n" ); document.write( "For the square root to be a whole number, a^3 must be divisible by 3, i.e. a=3,6,9 etc.
\n" ); document.write( "Try a=3 -> sqrt(27/3) = sqrt(9) = 3, which is prime
\n" ); document.write( "So x = 3^3/3 = 9
\n" ); document.write( "Ans: 9\r
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