Geometry

Make a conjecture for each scenario
The square root of an even number
The product of two odd numbers and a multiple of 2

Find one counterexample to show that each conjecture is false.
For two real numbers a and b, a is either equal to b or greater than b.
All quardrilaterals are parallelograms.

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  1. an even number k is of the form k=2m
    so, √(2m) = √2 * √m
    Now the only way to get rid of the pesky √2 is for m to also have a factor of 2. That is, m=2n
    √(2m) = √(2*2n) = √(4n) = 2√n
    Thus, for an even number to have an integer root, it must be a multiple of 4.

    What can you do on the others?

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