Properties of Square Numbers

If one side of a right angled triangle is $18 \mathrm{cm}$, find its other sides.(Use the concept of Pythagorean triplet)

Perfect square numbers ending with $\text{'}6\text{'}$ will have their square roots ending in $\_\_\_\_\_$.

The unit digit of the square of $19$ and $11$ is $1$.

Perfect square numbers ending with $\text{'}1\text{'}$ will have their square roots ending in $\_\_\_\_\_$.

The base and height of a right-angled triangle are $5\text{cm} \text{and} 12\text{cm}$ respectively. Find the third side and draw the right-angled triangle.

The base and height of a right-angled triangle are $3\text{cm} \text{and} 4\text{cm}$ respectively. Find the third side and draw the right-angled triangle.

Without actual addition, find the sum of the following.

$1+3+5+7+9+11+13+15+17+19$

Without actual addition, find the sum of the following.

$1+3+5+7+9+11+13+15$

Without actual addition, find the sum of the following.

$1+3+5+7+9+11+13$

The square of an odd number can always be written as the sum of two consecutive natural numbers. Can the reverse statement be true? Is the sum of any two consecutive natural numbers a perfect square of a number?

Consider the square number $1089$, express it as the sum of two consecutive positive integers.

Consider the square number $289$, express it as the sum of two consecutive positive integers.

Consider the following square number $225$, express it as the sum of two consecutive positive integers.

Consider the following square number $441$, express it as the sum of two consecutive positive integers.

Find the sum without actually adding the following odd numbers: $1+3+5+7+\dots \dots +35$

Find the sum without actually adding the first $99$ odd natural numbers.

Check whether given three numbers are Pythagorean triplets or not?

$10, 24, 26$

Check whether the following are Pythagorean triplets.
$8, 41, 40$

Check whether the following are Pythagorean triplets.
$264, 265, 23$
 

Check whether the following are Pythagorean triplets.
$57,176,185$