Question

Find the square of $71$ without multiplication.

Answer 1

Finding the square without multiplication

We can apply the identity ${(a+b)}^2=a^2+2ab+b^2$ to find the square of $71$.

We can write $71$ as $70+1$.

On applying the identity ${(a+b)}^2=a^2+2ab+b^2$ to find the square of $71$ , we get,

$$\begin{gathered} {\left(71\right)}^2 \\ ={(70+1)}^2 \\ ={\left(70\right)}^2+2\left(70\right)\left(1\right)+{\left(1\right)}^2 \\ =4900+140+1 \\ =5041 \end{gathered}$$
Hence, the square of $71$ is $5041$.