Question

Evaluate: $\frac{(0.013{)}^3+(0.007{)}^3}{(0.013{)}^2-0.013\times 0.007+(0.007{)}^2}$

• A. $0.020$
• B. $0.030$
• C. $0.150$
• D. $0.250$

Answer 1

The correct option is A $0.020$

$\frac{{\left(0.013\right)}^3+{\left(0.007\right)}^3}{{\left(0.013\right)}^2-(0.013\times 0.007)+{\left(0.007\right)}^2}$

Using $a^3+b^3=(a+b)(a^2-ab+b^2)$

$\Rightarrow \frac{a^3+b^3}{a^2-ab+b^2}=(a+b)$

$\Rightarrow a=0.013,$ $b=0.007$

$\Rightarrow \frac{{\left(0.013\right)}^3+{\left(0.007\right)}^3}{{\left(0.013\right)}^2-(0.013\times 0.007)+{\left(0.007\right)}^2}=(0.013+0.07)=\mathrm{0.02.}$

Hence, the answer is $\mathrm{0.02.}$