Simplify the following.

\(\frac{0.01 \times 0.01 \times 0.01 +0.003 \times 0.003 \times 0.003}{0.05 \times 0.05 - 0.015 \times 0.05+0.015 \times 0.015}\)

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SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 3)

Answer 1

Given:

\(\frac{0.01 × 0.01 × 0.01 +0.003 × 0.003 × 0.003}{0.05 × 0.05 - 0.015 × 0.05+0.015 × 0.015}\)

Formula used:

a³ + b³ = (a + b)(a² - ab + b²)

Calculation:

\(\frac{0.01 × 0.01 × 0.01 +0.003 × 0.003 × 0.003}{0.05 × 0.05 - 0.015 × 0.05+0.015 × 0.015}\)

⇒ (0.013 + 0.0033)/(5 × 0.01 × 5 × 0.01 - 5 × 0.01 × 5 × 0.003 + 5 × 0.003 × 5 × 0.003)

⇒ (0.013 + 0.0033)/(25 × 0.01 × 0.01 - 25 × 0.01 × 0.003 + 25 × 0.003 × 0.003)

⇒ (0.01³ + 0.003³)/25(0.012 - 0.01 × 0.003 + 0.0032)

⇒ (0.01 + 0.003)/25

⇒ 13/25 × 10- 3

∴ The value is 13/25 × 10^-3

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