Hi, I found out something interesting about perfect squares and I would like to share it.
I don't know if anyone knew this, but I believe that most of you might knew this.
This is a quite easier way to find the square of a large number
Alright, let's start with two unknowns. I'll take \(x\) and \(y\) while \(y = x+1\)
As we knew that \(x^2 = x\times x\) and \(y^2 = y\times y\), we can change \(y^2\) to be
\(y\times y = y(x+1) = y\times x + y\)
\(=x(x+1) + y = x\times x + x + y\)
\(=x^2 + x + y\)
\(y^2 = x^2+x+y\)
Now, we have a simplified version of \(y^2\)
Let's try \(x = 3\) and \(y = 4\)
\(4^2 = 3^2 + 3 + 4\)
\(16 = 9 + 3 + 4\)
And 16 is indeed equal to \(9 + 3 + 4\)
So it worked! Yeah!
Now let's try a larger number, 501
If \(y = 501, x = 500\)
\(501^2 = 500^2 + 500 + 501\)
\(501^2 = 250000 + 500 + 501\)
\(501^2 = 251001\)
Try it in your calculator and you will find it true
Alright, that's all. Thanks everyone for viewing this.
Try this problem to see if you understand it
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