Properties of Square Numbers

What will be the number of zeros in the square of $400$?

What will be the "one's digits" in the square of the following number?

$9106$

What will be the number of zeros in the square of $60$?

What will be the "one's digits" in the square of the following number?

$21222$

What will be the "one's digits" in the square of the following number?

$99880$

What will be the "one's digits" in the square of the following number?

$52698$

What will be the "one's digits" in the square of the following number?

$26387$

What will be the "one's digits" in the square of the following number?

$1234$

Find whether the square of the following number is odd number or an even number.

$1980$

Find whether the square of the following number is odd number or an even number.

$269$

Find whether the square of the following number is odd number or an even number.

$158$

Find whether the square of the following number is odd number or an even number.

$727$

Find the perfect square numbers between $50$ and $60$.

Find the perfect square numbers between $30$ and $40$.

Observe the pattern.

$7^2=49$

${67}^2=4489$

${667}^2=444889$

${6667}^2=44448889$

${66667}^2=4444488889$

${666667}^2=444444888889$

Write the square, making use of the above pattern: ${66666667}^2$

Observe the pattern.

$7^2=49$

${67}^2=4489$

${667}^2=444889$

${6667}^2=44448889$

${66667}^2=4444488889$

${666667}^2=444444888889$

Write the square, making use of the above pattern: ${6666667}^2$

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: ${1111111}^2$

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: ${111111}^2$

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. 

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