Properties of Square Numbers

Properties of square numbers are:

  • If a number has 0, 1, 4, 5, 6 or 9 in the unit’s place, then it may or may not be a square number. If a number has 2, 3, 7 or 8 in its units place then it is not a square number.
  • If a number has 1 or 9 in unit’s place, then it’s square ends in 1.
  • If a square number ends in 6, the number whose square it is, will have either 4 or 6 in unit’s place.

Square Root of a Number

Finding the number whose square is known is known as finding the square root. Finding square root is inverse operation of finding the square of a number.


Estimating Square Roots

Estimating the square root of 247:

Since: 100 < 247 < 400
i.e. 10 < \sqrt{247} < 20
But it is not very close.
Also, 15^2= 225  <247 and 16^2=256 > 247
15<\sqrt{247}<16.
256 is much closer to 247 than 225.
Therefore, \sqrt{247} is approximately equal to 16.

Numbers between Square Numbers

There are 2n non-perfect square numbers between squares of the numbers n and (n + 1), where is any natural number.

Example:

  • There are two non-perfect square numbers (2, 3) between 12=1 and 22 = 4.
  • There are four non-perfect square numbers (5, 6, 7, 8) between 22 = 4 and 32=9.

Pythagorean Triplets

2m, (m2−1) and (m2+1) forms a Pythagorean triplet.
For m = 2, 2m = 4, m2−1 = 3 and m2+1 = 5.
So, 3, 4, 5 is the required Pythagorean triplet.


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