Basic Concepts of Square

Basics of Squares

Quantitative Aptitude: Properties of Squares

Last Updated: Sep 19, 2019

Some Properties of  Square Numbers

  1. If a number has 0 in the unit’s place, then its square ends in 0.
    If a number has 1 or 9 in the unit’s place, then its square ends in 1.
  2. The square, if, ends in 4, then the number has 2 or 8 in the unit’s place.
  3. The number will have 3 or 7 in the unit’s place if the square ends in 9.
  4. The number will have 4 or 6 in the unit’s place if the square ends in 6.
  5. The square will end in 5 if the number has 5 in the unit’s place.
  6. A number ending with one zero will results in 2 zeros in its square. Those ending with two zeros will square itself and give four zeros and so. This means that a perfect square will always end in even number of zeros.
  7. The square of a number n is equal to the sum of first n odd natural numbers.
  8. The unit’s digit of the square of a natural number is the unit’s digit of the square of the digit at unit’s place of the given natural number.
  9. The Square of a natural number other than one is either a multiple of 4 or exceeds a multiple of 4 by 1.

Understanding the basics of square is necessary to solve questions that are asked in various competitive exams in the Quantitative Aptitude section - applicable to CAT, XAT, MAT, SNAP, IIFT, CLAT, AILET, DU LLB, any other entrance exam as well.
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