To find if given number is perfect square or not

Question might arises in your mind that how do we come to know if given number is the perfect square or not.

 for this, you can use various rules to assure if the number is not a perfect square. If the rules don't follow than the square may or may not be a perfect square so than go for trial and error by finding a square root.

1. Last Digit:
check if last digit of number is any other than  1,4,9,6,5. Then the number is not a perfect square.

2. Digital Root:
If the last digit is either of 1,4,9,6,5  than check the digital root of the number, if it ends up in digit other than  0,1,4,7,9 than that number is not a perfect square. (To learn how to find out digital root click here)

3. Tens digit:
 Now final step if above conditions satisfy than check  the tens digit
  • If the last digit is 5 than tens digit must be 2. If not then not a perfect square
  • If the last digit is 6 and the ten's digit is even then a number is not a perfect square.
  • If the last digit is 1,4,9 than tens digit must be even if not than the number is not a perfect square.

consider a number 56814

  1.  The last digit is 4 so it may be a perfect square.
  2. now digital root is  6. so it is not a perfect square.
consider another number 89149- Not perfect square


  1.   Now the last digit of a number is 4 . so it may be a perfect square 
  2.   Now digital root is 4 so it may be a perfect square  . 
  3.  Now the last digit is 9  so tens digit must be an even number here 4 is at tens place so  it may or may not be a  perfect  square. 

consider number 432964- a perfect square
  1. Last digit is 4 so it may be perfect square
  2.  digital root is 1 so it may be a perfect square.
  3. the last digit is 4  and tens place have even  value i.e. 6 so it may be a perfect square.

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