Multiplication By Patterns - 3

Algebra Level 1

$\begin{array} { r c l } 97 ^2 & = & 9409 \\ 997^2 & = & 994009 \\ 9997^2 & = & 99940009 \\ \end{array}$

What is $99997^2$ ?

1 solution

Nihar Mahajan
Mar 10, 2016

Note that every 99999....9997 can be expressed in the form $10^n-3$ for some integer $n>1$ . Let's see what happens when we square it:

$(10^n-3)^2 = 10^{2n} - 6\times 10^n + 9 = 10^n(10^n-6)+9$

Hence the general pattern for $n$ number of 9's is given by $10^n(10^n-6)+9$ and for this question , put $n=5$ :)

Yes! That's the explanation for the pattern :)

Chung Kevin - 5 years, 3 months ago

Thanks! Your questions are easy but quite interesting!

Nihar Mahajan - 5 years, 3 months ago