Before proceeding further on properties of square and square roots, take a glimpse on  definition of Square and Square root.

Square: If a number is multiplied by itself, then the result of this multiplication is called the square of that number.

Square Root: Square root of a number is that number, the square of which is equal to the given number.

 Different Properties of square and square roots

The difference of two consecutive numbers will always be equal to the sum of the number i.e., (a2 – b2) = (a+b)(a-b). Here, a>b and (a,b) being consecutive (a-b) = 1.

If a = 5 and b = 4, then (52 – 42) = (5+4)(5-4) = 9 * 1 = 9.

If the square of any number ends with 1, then its square root will end with 1 or 9.

If the square of number ends with 4, then its square root will end with 2 or 8.

If the square of any number ends with 5, then its square root will end with 5.

If the square of any number ends with 9, then its square root will end with 3 or 7.

The square of any number always ends with 0,1,4,5,6 or 9 but will never end with 2, 3, 7 or 8.

Square root of negative number is imaginary and that number is called complex number and the root which gives  negative root result is called complex root and the negative sign under the square root  is called "iota". 

Check: Methods to find square of number; Never ending infinite square root problem

 Important Relations for square and square root

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