Question

Evaluate the following without actual multiplication : ${\left(58\right)}^2$

Answer 1

We need to find the square of $58$ without doing $58\times 58$

Step 1 : We can write $58$ as $(60-2)$

Step 2 : Now calculate the square of $(60-2)$, using the identity ${(a-b)}^2=a^2-2ab+b^2$

$$\begin{gathered} {(60-2)}^2={\left(60\right)}^2-2\left(60\right)\left(2\right)+{\left(2\right)}^2 \\ =3600-240+4 \\ =3360+4 \\ =3364 \end{gathered}$$

Hence the square of $58$ is $3364$