Simplification of $$\frac{{{{\left( {3.4567} \right)}^2} - {{\left( {3.4533} \right)}^2}}}{{0.0034}} = ?$$

A. 6.91

B. 7

C. 6.81

D. 7.1

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {\text{According to the question}} \cr & {\text{ }}\frac{{{{\left( {3.4567} \right)}^2} - {{\left( {3.4533} \right)}^2}}}{{0.0034}} \cr & \left[ {\because {a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)} \right] \cr & \Rightarrow \frac{{\left( {3.4567 + 3.4533} \right)\left( {3.4567 - 3.4533} \right)}}{{0.0034}} \cr & \Rightarrow \frac{{6.91 \times 0.0034}}{{0.0034}} \cr & \Rightarrow 6.91 \cr} $$