Question

The square of which among the following numbers is a palindrome?

• A. ${122}^2$
• B. ${125}^2$
• C. ${127}^2$
• D. ${111}^2$

Answer 1

The correct option is D ${111}^2$

The word "Palindrome" stands for the numbers and strings that remain the same on reversing. For example, NAMAN, $1991$, etc.

$\bullet$ The square of $122$ is $122\times 122=14,884$. But when we reverse the square of $122$, we get $48,841,$ which is NOT the same as $14,884$. So, the square of $122$, i.e., ${122}^2=14,884$ is NOT a palindrome number.

$\bullet$ The square of $125$ is $125\times 125=15,625$. But when we reverse the square of $125$, we get $52,651,$ which is NOT the same as $15,625$. So, the square of $125$, i.e., ${125}^2=15,625$ is NOT a palindrome number.

$\bullet$ The square of $127$ is $127\times 127=16,129$. But when we reverse the square of $127$, we get $92,161,$ which is NOT the same as $16,129$. So, the square of $127$, i.e., ${127}^2=16,129$ is NOT a palindrome number.

$\bullet$ Finally, we need to find the value of ${111}^2$.
$\square$ $111$ consists of three $1$'s;
$\square$ Write starting from $1$ till the number of $1$'s; hence, $\underset{–}{123}$;
$\square$ Concatenate the reverse counting upto $1$ with the last digit; hence, $123\underset{–}{21}$
$\therefore \underset{–}{{111}^2=12,321}$

So, the square of $111$ is $12,321$. When we reverse the square of $111$, we get $12,321,$ which is same as the original number.
$\therefore {111}^2=12,321$ is a palindrome number.

Therefore, option (d.) is the correct answer.