The value of $$\frac{(5.4)^3 - 0.064}{(5.4)^2 + 2.16 + 0.16}$$ is:​

Correct option is B

To solve:

​$$\frac{(5.4)^3 - 0.0064}{(5.4)^2 + 2.16 + 0.16}$$

Formula used:

​$$(x^3 - y^3) = (x - y)(x^2 + xy + y^2)$$​​

Solution:

​$$\begin{aligned}&\frac{(5.4)^3 - 0.064}{(5.4)^2 + 2.16 + 0.16} \\&\Rightarrow \frac{[(5.4)^3 - (0.4)^3]}{[(5.4)^2 + 2.16 + (0.4)^2]} \\&\Rightarrow \frac{(5.4 - 0.4)[(5.4)^2 + 2.16 + (0.4)^2]}{[(5.4)^2 + 2.16 + (0.4)^2]} \\&\Rightarrow 5.4 - 0.4 = 5\end{aligned}$$

Hence, option (b) is the correct answer.