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Because anything times itself equals a perfect square and is considered that taking the square root of a perfect square (non negative numbers) which end result does not involve fractions but whole numbers is a perfect square. 1 x 1 = 1 sq.root(1) = 1 2 x 2 = 4 (Perfect square) sq.root(4) = 2
A perfect number is the sum of its divisors; for example 6 is a perfect number because the sum of its divisors is 6 (1 + 2 + 3). The sum of the divisors of 8 is 7 (1 + 2 + 4), so 8 is not a perfect number.
He discovered the ratio of a perfect octave is 2:1.
There is only one Perfect Number within this range : 496. If 2ⁿ - 1 is prime then 2ⁿ⁻¹(2ⁿ - 1) is a perfect number. In this instance n = 5 then, 2⁴(2⁵ - 1) = 16 x 31 = 496...........and 31 is a prime number.
The squares of whole numbers are called perfect squares. A perfect square is a number that can be expressed as the product of an integer multiplied by itself. For example, 1, 4, 9, 16, and 25 are perfect squares because they can be written as 1^2, 2^2, 3^2, 4^2, and 5^2, respectively.