Find the square root of $5929$ by prime factorisation.

Find the square root of $9216$ by prime factorisation. 

Find the square root of $7744$ by prime factorisation.

Without doing any calculation, check whether $257$ maybe a perfect square or is surely not a perfect square.

Without doing any calculation, check whether $153$ maybe a perfect square or is surely not a perfect square.

Without doing any calculation, find if $441$ maybe a perfect square or is surely not a perfect square.

Without doing any calculation, check whether $408$ may be a perfect square or is surely not a perfect square.

Find the smallest prime number by which $2028$ should be multiplied so as to get a perfect square number. Also, find the square root of the number so obtained.

Find the smallest prime number by which $1008$ should be multiplied so as to get a perfect square number. Also, find the square root of the number so obtained.