Question

Stuart decides there are no odd square numbers. His justification is that ‘because an even number multiplied by an even number produces an even number, and that an odd number multiplied by an odd number also produces an even number, then there are no odd square numbers’. Do you agree with Stuart’s claim? If not, give an example to explain your answer. Please explain

Answer 1

this is false because 3 times 3=9 and all of those are odd
odd nubmers are represented by 2n+1 where n= a natural number (whhole numbers and negatives)
so (2n+1) squared=(2n+1)(2n+1)=4n^2+4n+1
(a whole number times an even number yeilds an even number because an even number is represented by 2n where n=a natrual number so 2n times x=2nx which is still even.)
since n represents a whole number and a whole number times an even number (4) equals an even number, 4n^2 and 4n must be even, and even+even=even
that leavs the +1 at the end
we know that even+1=odd so therefor any odd number squared results in an odd nnumber




an example is 9, 3 times 3 or 3 squared