How many non-perfect square numbers lie between the squares of the following numbers?

$27$ and $28$

How many non-perfect square numbers lie between the squares of $101$ and $102$?

Observe the following pattern.

$$\begin{gathered} 2^2-1^2=2+1; \\ {3}^2-2^2=3+2; \\ {4}^2-3^2=4+3; \\ {5}^2-4^2=5+4 \end{gathered}$$

Now, find the value of ${136}^2-{135}^2$ 

Observe the following pattern.

$$\begin{gathered} 2^2-1^2=2+1; \\ {3}^2-2^2=3+2; \\ {4}^2-3^2=4+3; \\ {5}^2-4^2=5+4 \end{gathered}$$

Now, find the value of ${98}^2-{97}^2$ 

Observe the following pattern.

$$\begin{gathered} 2^2-1^2=2+1; \\ {3}^2-2^2=3+2; \\ {4}^2-3^2=4+3; \\ {5}^2-4^2=5+4 \end{gathered}$$

Now, find the value of the ${121}^2-{120}^2$ .

Observe the following pattern and fill in the missing numbers.

$$\begin{gathered} 1^2=1 \\ {2}^2=1+3 \\ {3}^2=1+3+5 \\ {4}^2=1+3+5+7 \\ {5}^2=1+3+5+7+9 \\ ⋮ \\ {9}^2=1+3+5+7+9+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_ \\ ⋮ \\ \_\_\_\_\_=1+3+5+7+9+11+13+15+17+19+21 \end{gathered}$$

Write a Pythagorean triplet whose smallest member is $16$.

Write a Pythagorean triplet whose smallest member is $14$.

Write a Pythagorean triplet whose smallest member is $20$.