He's a maths problem I am stuck with... Thanks for your help in advance.
List the digits that will not be in the units' digit of any square number? (please show clear reasoning)
He's a maths problem I am stuck with... Thanks for your help in advance.
List the digits that will not be in the units' digit of any square number? (please show clear reasoning)
Hi Natasha1
When you multiply 2 numbers together you can always tell what the last digit is going to be just by looking at the last digits of the initial 2 numbers.
eg $\displaystyle 3129\times123750856 \text{ will end in a 4 because } 9\times 6=54 \text { and 54 ends in a 4 } $
with this knowledge you can work out what are the possible last digits of squared numbers can be and hence, what digits they cannot be.
Well, proofs are definitely not my forte but I can at least give you more of an explanation
$\displaystyle \begin{align*}\text{Let y }&=(10a+x) \text{ where }a, x, \text{ and therefore y are in the set of integers greater or equal to zero, also } x<10\\y^2&=100a^2+20ax+x^2\\y^2&=10(10a^2+2ax)+x^2 \end{align*}$
so, the last digit will be the last digit of $\displaystyle x^2$
OR
If you think about how long multplication works you can also 'see' that this will be true.
Is this enough or are you after a formal proof?