1.  Which of the following numbers are perfect squares   121,111,32,16
  2.  Which of the following numbers are squares of even numbers       225,373758,6561
  3.  Using prime-factorization method, find which of the following numbers are perfect square 225,2916,11025
  4. By just examing the unit digits,can you tell which of the following cannot be whole squares? 1022,1026,1027
  5. By what number should each of the following numbers be multiplied to get a perfect square in each case? Also. find the number  whose,square is the new number?  7776,2880,8820,605,
  6. By what number should each of the following be divided to get a perfect square in each case? also find the number whose square is the new number 16562,1575,5103

Hi!
Here is the answer to your question.
 
(3)
Consider the number 225.
 
 
 
Prime factorization of 11025 = 3 × 3 × 5 × 5 × 7 × 7
 
Since all the factors are in pairs, so 11025 is a perfect square.
 
(4)
The square numbers always ends in 0, 1, 4, 5, 6 or 9.
The unit digit of 1022 is 2. So, 1022 is not a perfect square.
The unit digit of 1026 is 6. But this number is not a perfect square (Number which end in 6 are not always perfect squares).
2116 is a perfect square.
The unit digit of 1027 is 7. So, 1027 is not a perfect square.
 
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