Question

What is square of $42$ without actual multiplication.

Answer 1

Given, the number is $42$.

We need to square the number $42$.

Step$1$: expand the number

$42=(40+2)$

${42}^2={\left(40+2\right)}^2$

Step $2$:using identity, ${(a+b)}^2=a^2+b^2+2ab$

where $a=40$ and $b=2$

Now, we get;

$$\begin{gathered} {\left(42\right)}^2={\left(40+2\right)}^2 \\ {\left(42\right)}^2={40}^2+2^2+2\times 40\times 2 \\ {\left(42\right)}^2=1600+4+160 \\ {\left(42\right)}^2=1764 \end{gathered}$$

Therefore, the square of $42$ is $1764$.