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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.
What is the smallest whole number that is a perfect square a perfect cube and a perfect fifth power?
the answer is definitly 0 (zero)!
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 is the smallest positive integer that 248832 can be multiplied by in order for the product to be a perfect square?
The prime factorisation of 248832 is 2¹⁰ × 3⁵ Every perfect square number has a prime factorisation where each prime is to an even power. 2 has an even power 3 has an odd power, so need an extra power → multiple 248832 by 3 which gets (2⁵ × 3³)²
What is a Perfect square that is a power of 2?
8
What is the smallest positive integer which you can multiply to 5688 to make it a perfect square?
In the prime factorisation of a perfect square in power format, all primes must be to an even power. 5688 = 23 x 32 x 79 To convert this it a perfect square, it needs the 2 and 79 to have an even power - the 3 is already at an even power. The smallest way to do this is to multiply 5688 by 2 x 79, ie multiply it by 158. 5688 x 158 = 23 x 32 x 79 x 2 x 79 = 24 x 32 x 792 = (22 x 3 x 79)2 = (948)2 = 898704
What is the perfect square to 360?
Three to the seventh power
What is a Perfect square that is a power of 2 for 9?
81
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 the perfect square of 4 using the power 2?
16
What is a 3-digit perfect square that is a power of 2?
1
