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What is the smallest number that divides 2880 to give a perfect square?
Divide 2880 by 5 to give the perfect square 576 = 242. First write 2880 in its prime factorisation in power form: 2880 = 26 x 32 x 51 To be a perfect square, all the prime factors need to have an even power, so to find the smallest number by which to divide to get a perfect square only all the odd powers need to be reduced by 1; only the power of the prime factor 5 is odd and needs to be reduced by 1, so divide by 5.
What are the 2 smallest whole numbers that are both a perfect square and a perfect cube?
0, 1To be both a square and a cube, the number has to be a sixth power. You don't need to calculate though, since 06=0 and 16=1.The next 2 sixth powers are 26=64 and 36=729.
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.
Can a square root of a perfect square be another perfect square?
Sure. Take the fourth power of any natural number, for example 24 = 16. It square root is a perfect square, in this case 22. As another example, the square root of 34 = 32.
What is a whole number raised to the second power?
It is the perfect square of that number.
