Question

Evaluate: $\frac{0.06\times 0.06\times 0.06-0.05\times 0.05\times 0.05}{0.06\times 0.06+0.06\times 0.05+0.05\times 0.05}$

• A. $0.01$
• B. $0.001$
• C. $0.1$
• D. $0.02$

Answer 1

The correct option is A $0.01$

We know that one of the identity of polynomials is:

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

Now let us substitute $a=0.06$ and $b=0.05$ in the above identity as follows:

$(0.06{)}^3-(0.05{)}^3=(0.06-0.05)\left\{\right(0.06{)}^2+(0.06\times 0.05)+\left(0.05{)}^2\right\}$

$\Rightarrow 0.06\times 0.06\times 0.06-0.05\times 0.05\times 0.05=0.01\times (0.06\times 0.06+0.06\times 0.05+0.05\times 0.05)$ .....(1)

Now consider the given expression as shown below:

$\frac{0.06\times 0.06\times 0.06-0.05\times 0.05\times 0.05}{0.06\times 0.06+0.06\times 0.05+0.05\times 0.05}$

$=\frac{0.01\times (0.06\times 0.06+0.06\times 0.05+0.05\times 0.05)}{0.06\times 0.06+0.06\times 0.05+0.05\times 0.05}$ ...From eqn (1)

$=0.01$