Question

Evaluate:  \(\sqrt[3]{0.3\space \times \space0.3\space \times\space 0.3 \space+\space 0.06\space \times \space0.06\space \times \space0.06\over0.6\space \times\space 0.6\space \times\space 0.6 \space+ \space0.12\space \times\space 0.12\space\times\space 0.12 }\)
1. 0.036
2. 0.125
3. 0.5
4. 1

Answer 1

Correct Answer - Option 3 : 0.5

Concept used:
In this type of question, we simplify the equation by taking two values as a and b and the remaining two which are their twice become 2a and 2b.

Calculation:
\(\sqrt[3]{0.3\space × \space0.3\space ×\space 0.3 \space+\space 0.06\space × \space0.06\space × \space0.06\over0.6\space ×\space 0.6\space ×\space 0.6 \space+ \space0.12\space ×\space 0.12\space×\space 0.12 }\)
Let 0.3 and 0.06 be a and b respectively.
⇒ 0.6 = 2 × 0.3 = 2a
⇒ 0.12 = 2 × 0.06 = 2b
⇒ (a³ + b³)/(2a × 2a × 2a + 2b × 2b × 2b)
⇒ (a3 + b3)/(8a³ + 8b³)
⇒ (a3 + b3)/[8(a3 + b3)]
⇒ 1/8
⇒ \(\sqrt[3]{0.3\space × \space0.3\space ×\space 0.3 \space+\space 0.06\space × \space0.06\space × \space0.06\over0.6\space ×\space 0.6\space ×\space 0.6 \space+ \space0.12\space ×\space 0.12\space×\space 0.12 }=\sqrt[3]{1\over8}\)
⇒ 1/2
⇒ 0.5
∴ The value is 0.5.