Find the value of the given expression correct upto 2 decimal places.

\(\frac{0.05 \times 0.05 \times 0.05+0.04 \times 0.04 \times 0.04 }{0.05 \times 0.05-0.05 \times 0.04+0.04 \times 0.04}\)

Given:

\(\frac{0.05 \times 0.05 \times 0.05+0.04 \times 0.04 \times 0.04 }{0.05 \times 0.05-0.05 \times 0.04+0.04 \times 0.04}\)

Formula Used:

a³ + b³ = (a + b)(a² - ab + b²)

Calculation:

\(\frac{0.05 \times 0.05 \times 0.05+0.04 \times 0.04 \times 0.04 }{0.05 \times 0.05-0.05 \times 0.04+0.04 \times 0.04}\)

⇒ \(\frac{(0.05)^3 +(0.04)^3}{(0.05)^2-0.05 \times 0.04+(0.04)^2 }\)

⇒ \(\frac{(0.05 +0.04)((0.05)^2-0.05 \times 0.04+(0.04)^2)}{(0.05)^2-0.05 \times 0.04+(0.04)^2 }\)

⇒ (0.05 + 0.04)

⇒ 0.09

∴ Option 2 is the correct answer.