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What numbers always have an even number of factors?
All positive integers which are not perfect squares.
Are all perfect squares rational?
Yes
Ratio of square numbers to numbers with 4 factors?
As N approaches infinity the ratio of squares less than N to numbers with 4 factors less than N approaches 0. This means that in the customary way of defining it, the ratio you're interested in is 0 (although that should be taken with a grain of salt - it certainly doesn't mean that there are 0 square numbers). The number of squares less than N is approximately √N. Rather than calculating the ratio we're interested in, we're going to calculate a calculate a ratio guaranteed to be greater: the ratio of squares to numbers that are twice a prime number (which are some, but not all, of the numbers with 4 factors). There are approximately N/ln N prime numbers less than N, by the prime number theorem. So there are N/(2 ln N/2) prime numbers less than N/2, which can be doubled to get a number less than N that's twice a prime number. The ratio is therefore √N(2 ln N/2)/N, which is O(ln N/√N). √N grows much faster than ln N, and in the limit this ratio will get close to zero. So the ratio we're actually interested in, which is even less than this ratio, will also approach zero.
Are perfect squares all rational numbers?
Yes.
How the ratio of volume is related to ratio of sides of similar cubes?
The ratio of volumes is directly proportional to the cube of the ratio of their sides. And, incidentally, all cubes are similar.
What kind of shapes are square but not a quadrilaterals?
There are no such shapes because all squares are quadrilaterals - by definition.
What kind of 2d shapes have all sides equal?
Squares
Make fifteen shapes. One fifth of the shapes are circles. One fifth of the shapes are triangles. Two fifth of the shapes are rectangles. The rest are squares How many shapes are rectangles and squares?
9 (six rectangles = three squares)
What is the relationship among these shapes triangle squares rectangles parallelograms quadrilaterals pentagon hexagon and octagon?
They are all polygons and they are shapes they all have sides and vertices. They all have a measure like how squares have 90 degrees angles.
How many different shapes can you make with 5 squares and they can't be the same when you turn it and all the shapes have to touch?
12
What shapes are all of the faces in a rectangular prism?
4 rectangles and 2 squares.
Why are all squares similar?
Because they are cooresponding shapes
What are all the shapes in geometry?
There are a great many different shapes that are in Geometry. There are squares, circles, triangles, rhombus', and hexagons for example.
What are all the shapes that look like a square?
All of them are squares.
Are all shapes with 4 sides the same shape?
No, there are squares, rectangles,trapezoids etc.
What shapes make a cube?
6 SQUARES arranged in a 3-dimensional form , make a CUBE .
What shapes have rotational symmetry?
squares
