^{2}

^{2}= (6 + 1)

^{2}= 7

^{2}= 49

This has something to with quadratic equations

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Kevin F. | Computer Programming and Mathematics TutorComputer Programming and Mathematics Tut...

If n is a perfect square, then the square root of n is an integer. For example, if n = 36, then the square root of n = 6. The next perfect square then is:

(√n + 1)^{2}

Staying with the example of n = 36, the square root of n = 6, and the expression yields:

(√36 + 1)^{2} = (6 + 1)^{2} = 7^{2} = 49

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

n^2 = ∑^{n} (2n_{i} + 1 ) / Square of any number n equals Sum of the Odd numbers from 1 to n

i=0

i.e. 3^2 = 1 + 3 + 5 =9

Next square number to n^2 equals n^2 +2n +1

ie. 3 ^2 = 9 9 + 2(3) +1= 16 = 4^2 .

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