Question

The value of $\frac{(2.3{)}^3-0.027}{(2.3{)}^2+0.69+0.09}$is:

• A. $2$
• B. $2.327$
• C. $3$
• D. $2.273$

Answer 1

The correct option is A

$2$

Finding value of given expression:

The given expression is $\frac{(2.3{)}^3-0.027}{(2.3{)}^2+0.69+0.09}$.

We know identity, $a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$.

The given expression can be rewritten as:

$\frac{(2.3{)}^3-0.027}{(2.3{)}^2+0.69+0.09}=\frac{(2.3{)}^3-{\left(0.3\right)}^3}{(2.3{)}^2+\left(0.3\right)\left(2.3\right)+{\left(0.3\right)}^2}$

Also, ${\left(2.3\right)}^3-{\left(0.3\right)}^3=\left(2.3-0.3\right)\left[{\left(2.3\right)}^2+\left(0.3\right)\left(2.3\right)+{\left(0.3\right)}^2\right]$

Substituting value we get:

$$\begin{gathered} \frac{(2.3{)}^3-(0.3{)}^3}{(2.3{)}^2+(0.3\left)\right(2.3)+(0.3{)}^2}=\frac{(2.3-0.3)\left[(2.3{)}^2+(0.3\left)\right(2.3)+(0.3{)}^2\right]}{(2.3{)}^2+(0.3\left)\right(2.3)+(0.3{)}^2} \\ =2 \end{gathered}$$

Hence option A is correct.