Question

Evaluate the following without actual multiplication : ${\left(298\right)}^2$

Answer 1

We need to find the square of $298$ without doing $298\times 298$

Step 1 : We can write $298$ as $(300-2)$

Step 2 : Now calculate the square of $(300-2)$, using the identity ${(a-b)}^2=a^2-2ab+b^2$

$$\begin{gathered} {(300-2)}^2={\left(300\right)}^2-2\left(300\right)\left(2\right)+{\left(2\right)}^2 \\ =90000-1200+4 \\ =88800+4 \\ =88804 \end{gathered}$$

Hence the square of $298$ is $88804$