Check whether the given number $784$ is a perfect square. If not, find the smallest number by which it should be divided so that the quotient is a perfect square.

 

Check whether the given number $1682$ is a perfect square. If not, find the smallest number by which it should be divided so that the quotient is a perfect square.

Check whether the given number $1728$ is a perfect square. If not, find the smallest number by which it should be divided so that the quotient is a perfect square.

Observe the following pattern and fill in the blanks:

$$\begin{gathered} 5^2=0\times 100+5^2=25 \\ {15}^2=1\times 200+5^2=225 \\ {25}^2=2\times 300+5^2=625 \end{gathered}$$

${35}^2=$ _____ $=1225$

${45}^2=4\times 500+5^2=$_____

_____${}^2=5\times 600+5^2=$_____

${65}^2=$_____ $=$_____ 

Write $7^2+8^2+{56}^2$ as square of a number. 

Write ${43}^2$ as square of $3$ numbers. 

Write the following sum as square of a number without any calculation.

$1+2+3+4+5+4+3+2+1$

Write the following sum as square of a number without any calculation.

$1+2+3+4+5+6+7+6+5+4+3+2+1$

Check whether the following triplet is Pythagorean triplet or not.

$\left(12,35,37\right)$