Question

Evaluate the following without actual multiplication : ${\left(72\right)}^2$

Answer 1

We need to find the square of $72$ without doing $72\times 72$

Step 1 : We can write $72$ as $(70+2)$

Step 2 : Now calculate the square of $(70+2)$, using the identity ${(a+b)}^2=a^2+2ab+b^2$

$$\begin{gathered} {(70+2)}^2={\left(70\right)}^2+2\left(70\right)\left(2\right)+{\left(2\right)}^2 \\ =4900+280+4 \\ =5180+4 \\ =5184 \end{gathered}$$

Hence the square of $72$ is $5184$