Question

Using identities, evaluate ${71}^2$

Answer 1

To evaluate :${71}^2$

${71}^2$ can be written as ${(70+1)}^2$

Using the identity

${(\mathrm{a}+\mathrm{b})}^2={\mathrm{a}}^2+{\mathrm{b}}^2+2\mathrm{ab}$

$\begin{array}{rcl}{\left(71\right)}^2& =& {(70\hspace{0.17em}+1)}^2\\ {\left(71\right)}^2& =& {70}^2+1^2+2\times 70\times 1\\ {\left(71\right)}^2& =& {70}^2+1^2+140\\ {\left(71\right)}^2& =& 4900+1+140\\ {\left(71\right)}^2& =& 5041\\ \therefore {71}^2& =& 5041\end{array}$