Which of the following numbers,wherein some o | vedclass

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(A) $1$. The square of an odd number must end in an odd digit $(1, 5, 9)$. Option $C$ ends in $4$,which is even,so it is eliminated.$2$. $A$ $3$-digit

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$65xxx1$

Vedclass · Answer

(A) $1$. The square of an odd number must end in an odd digit $(1, 5, 9)$. Option $C$ ends in $4$,which is even,so it is eliminated.$2$. $A$ $3$-digit number $n$ ranges from $100$ to $999$. The square $n^2$ ranges from $100^2 = 10,000$ to $999^2 = 998,001$.$3$. Therefore,the square of a $3$-digit number must have either $5$ or $6$ digits.$4$. Option $A$ $(65xxx1)$ has $6$ digits,which is possible.$5$. Option $B$ $(9xx1)$ has only $4$ digits,which is impossible for a $3$-digit number.$6$. Option $D$ $(9xxxxxx5)$ has $8$ digits,which is impossible for a $3$-digit number.$7$. Thus,$65xxx1$ is the only possible candidate.

Which of the following numbers,wherein some of the digits have been suppressed by symbols,can possibly be the perfect square of a $3$-digit odd number?

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