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

${40}^2$ and ${41}^2$.

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

${80}^2$ and ${81}^2$.

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

${101}^2$ and ${102}^2$.

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

${205}^2$ and ${206}^2$.

Observe the pattern in the following and find the missing numbers.

$$\begin{gathered} 121=\frac{{\left(22\right)}^2}{1+2+1} \\ 12321=\frac{{\left(333\right)}^2}{1+2+3+2+1} \\ 1234321=\mathrm{\_\_\_\_\_} \\ 123454321=\mathrm{\_\_\_\_\_} \\ 12345654321=\mathrm{\_\_\_\_\_} \end{gathered}$$

Which of the following triplets are Pythagorean?

$(3, 4, 5), (6, 7, 8), (10, 24, 26), (2, 3, 4)$.

Find the square root of the following numbers by the repeated subtraction method.

$16$

Find the square root of the following numbers by the repeated subtraction method.

$49$.

Find the square root of the following numbers by the repeated subtraction method.

$64$.