To find a number that is both a perfect square and a perfect cube, we must solve x2 = x3 over x ∈Z+. The only two solutions to this equation are 0 and 1, or x = {0,1}. Therefore, zero and one are the only two numbers that are both perfect squares and perfect cubes.
--In easier terms: a perfect square is a number that can be "square rooted" and have no remainder. Like, 144. The square root is 12 therefore 144 is a perfect square. A perfect Cube is the same except that it must be "cubed rooted". Like 27. The cube root of this number is 3 therefore 27 is a perfect cube.
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7 cubed is 343
If by 'perfect number' you mean 'perfect SQUARE', then yes. 49 is an odd number and a perfect square.
You take the square root of the number. If it is a perfect square, this will be a whole number. If it is not, it isn't a perfect square.
Well, technically, it is the square of 11.18033989...but it is not a perfect square(a perfect square is the square of a whole number. 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256, etc.)
27 is a not perfect square.