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What whole number is less than 100 that is both a perfect square and a perfect cube?
To be a perfect square, all the primes in a number's prime factorisation must have an even power To be a perfect cube, all the primes in a number's prime factorisation must a power that is a multiple of 3 → To be a perfect square, all the primes in a number's prime factorisation must a power that is a multiple of 3 and a multiple of 2, ie the power must be a multiple of 6 The smallest prime is 2 2⁶ = 64 = (2³)² = 8² = (2²)³ = 4³ 2¹² = 4096 (too large) 3⁶ = 729 (too large) There is also 1 = 1² = 1³ Thus the whole numbers less than 100 which are both perfect squares and perfect cubes are 1 and 64.
There is only one perfect cube number less than 200 whose square root is rational Write down that number?
There are two answers 1 and 64
The only cube that is one less than a square?
eight
Which number is the only cube one less less than a square?
eight ( 8 )
Is there a prime number where there is 1 less than a perfect square?
3 is prime, 1 less than the perfect square of 4 (2x2)
