Check whether the following number is a perfect square or not:
$49$

Express the following as the sum of two consecutive integers: ${21}^2$

Express the following as the sum of two consecutive integers: ${13}^2$

Express the following as the sum of two consecutive integers: ${11}^2$

Express the following as the sum of two consecutive integers: ${19}^2$

Do you think the reverse is also true, i.e., is the sum of any two consecutive positive integers is perfect square of a number? Give example to support your answer. 

Observe the pattern.

$1^2=1$

${11}^2=121$

${111}^2=12321$

${1111}^2=1234321$

${11111111}^2=123456787654321$

Write the square, making use of the above pattern: ${111111}^2$

Observe the pattern.

$1^2=1$

${11}^2=121$

${111}^2=12321$

${1111}^2=1234321$

${11111111}^2=123456787654321$

Write the square, making use of the above pattern: ${1111111}^2$