Question

Evaluate ${\left(52\right)}^2$ using suitable identities

Answer 1

Given expression can be written as

${\left(52\right)}^2={(50+2)}^2$

We know that

${(a+b)}^2=a^2+2ab+b^2$

Here

$a=50,b=2$

$$\begin{gathered} \Rightarrow {(50+2)}^2={50}^2+2\times 50\times 2+2^2 \\ =2500+200+4 \\ =2704 \end{gathered}$$

Hence, we get $2704$ after simplification