This chapter manages square numbers properties, intriguing patterns that could be mastered utilizing square numbers, finding the square of a number, Pythagorean triplets, discovering square roots through different strategies.
Properties of Square Numbers
Square Root of a Number
Finding the number whose square is given is called the square root, whereas, finding the square root is the inverse function of finding the square of a number. If a perfect square has 'n' digits, its square root will have 'n/2' digits if 'n' is even and '(n+1)/2' digits if n is odd. If a natural number m can be represented as n2, where n is also a natural number, then m is a square number.
Finding the Square of a Number
If the alphabet n is a number, then its square is given as n×n=n2. Squares of certain numbers having two or more digits can be found by writing the number as the sum of two numbers. Consequently, if we add two consecutive triangular numbers, we get a square number.
Numbers between Square Numbers
Consequently, there are 2n non-perfect square numbers between squares of the numbers n and (n + 1); where n is any natural number.
Addition of Odd Numbers
Addition of first n odd natural numbers is n2.
Square of an Odd Number
Square of an odd number denoted by n can be expressed as the sum of two consecutive positive integers (n2 −1)/2 and (n2 +1)/2
For any natural number where m>1, we have (2m)2 + (m2−1)2 = (m2+1)2.
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