Question

Find the square of $105$ using an identity.

Answer 1

Find the square using an identity.

We can write $105$ as $100+5$.

On applying the identity ${(a+b)}^2=a^2+2ab+b^2$ to find the square of $105$ , we get,

$$\begin{gathered} ={(100+5)}^2 \\ ={\left(100\right)}^2+2\left(100\right)\left(5\right)+{\left(5\right)}^2 \\ =10000+1000+25 \\ =11025 \end{gathered}$$
Hence, using an identity, the square of $105$ is $11025$.