Monday, 30 April 2012

Trick to identify exact squares

While vedic math tricks would make squaring numbers very easy, these few tricks help identify perfect squares merely by observing the number.:


Structure of the square root:
First trick is to understand what would be the structure of the square root just by observation.

  • The number of digits before decimal point would reduce to half when we take the square root of the number.(i.e. the square root of 1446.78 would have 2 digits before decimal number). This math trick would be applicable directly when the numbers of digits before decimal point are even.
  • In case of odd number of digits before decimal point, the square root would still have half of the numbers but that half needs to be rounded up to the next integer. (i.e. square root of 144.678 would have two digits before the decimal point.)
  • The number of digits after the decimal point would reduce to half when we take the square root of the number.(i.e. the square root of 1446.78 would have 1 digits after decimal number). This math trick would be applicable directly when the numbers of digits before decimal point are even.
  • For numbers with odd digits after decimal point, the square root would be an irrational number, because any square of a whole rational number would have even digits only after the decimal point.
Nature of the square root:Next trick is to know the type of answer to expect while trying to derive square root of a number, the rule is:
  • For the numbers not exact squares of another whole number, their square root is always irrational. (i.e. the square root would have endless digits after decimal point and would not have any repeating patters in those digits.)
  • Also, a number is odd number of zero's at the end, would never have a rational square root
  • For the rest of the numbers the square root would be rational.
The last digit of the answer:This is a trick to identity an exact square and also to estimate the last digit of the square root.
  • Number with last digits as 2, 3, 7 or 8 are not exact squares and inturn would result in an irrational number when their square root is calculated
  • Also, there is a direct relation between last digit of the number and last digit of its square root, as follows:
    • number 1, square root 1 or 9
    • number 4, square root 2 or 8
    • number 5, square root 5
    • number 6, square root 4 or 6
    • number 9, square root 3 or 7
  • When the second last digit (from right) is even and the last digit is 6, the number is not a perfect square (i.e. 346 is not a perfect square)
  • When the second last digit (from right) is odd, the last digit has to be 6 for the number to be a perfect square. (i.e. numbers ending with 34, 59, 11 are not perfect squares)
  • When a number is even, and its last two digits taken together are not divisible by 4, that number is not a perfect square. (i.e. numbers ending with 42, 86, etc. are not perfect squares)
Odd one out:This trick will tell us whether the square root would be even or odd.

  1. Square root is odd when a perfect square is odd
  2. Square root is even when a perfect square is even
These tricks would be particularly helpful when attempting multiple choice questions or math puzzles relating to squares or square roots.

2 comments:

  1. This makes it very easy to attempt competitive exams with MCQ. Thanks a lot bro

    ReplyDelete
  2. what about if no is 56 or 76?

    ReplyDelete