Question

The solution of the following by using suitable identities:
${509}^2$ is ------

Answer 1

The given expression ${509}^2$ can be rewritten as $(500+9{)}^2$ and we solve it as follows:

$(500+9{)}^2=(500{)}^2+(9{)}^2+(2\times 500\times 9)(\because (a+b{)}^2=a^2+b^2+2ab)=250000+81+9000=259081$

Hence, ${509}^2=259081$.