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**Introduction**

**Square of a number students are advised to commit to memory.**

**Perfect square or square number A natural number n is called a perfect square or a square number if there exists a natural number m such that `n = m^2`.**

**Show that 63504 is a perfect square. Also find the number whose square is 63504.**

**Find the smallest number by 180 must be multiplied so that the product is a perfect square.**

**Property 1 A number having `2,3,7 or 8` at units place is never a perfect square. In other words no square number end in `2,3,7 or 8`.**

**Property 2 The number of zero at the end of a perfect square is always even.**

**Property 3 Square of even numbers are always even numbers and squares of odd numbers are always odd numbers.**

**Property 4 The square of a natural number other than one is either a multiple of 3 or exceeds a multiple of 3 by 1.**

**Property 5 The square of a natural number other than one is either a multiple of 4 or exceeds multiple of 4 by 1.**