Question

Using identities, evaluate $10.5x9.5$

Answer 1

Product of number using identity:

To Evaluate : $10.5x9.5$

$10.5$ can be written as $(10+0.5)$ and $9.5$ can be written as $(10–0.5)$

$$\begin{gathered} 10.5x9.5=(10+0.5)(10–0.5) \\ \Rightarrow (10+0.5)(10–0.5)=100–0.25\mathbf{\left[}\mathbf{\because }\mathbf{(}\mathbf{a}\mathbf{+}\mathbf{b}\mathbf{)}\mathbf{(}\mathbf{a}\mathbf{-}\mathbf{b}\mathbf{)}\mathbf{=}{\mathbf{a}}^{\mathbf{2}}\mathbf{-}{\mathbf{b}}^{\mathbf{2}}\mathbf{\right]} \\ \Rightarrow (10+0.5)(10–0.5)=100–0.25 \\ \Rightarrow (10+0.5)(10–0.5)=99.75 \\ \Rightarrow (10+0.5)(10–0.5)=99.75 \end{gathered}$$

$\therefore 10.5x9.5=99.75$

Hence,the value $10.5x9.5$ is $99.75$