Question

The value of \( \left( \sqrt{\frac{5}{13}} \right) \left( \frac{14}{25} \right) + 2 \times \frac{3}{10} - \frac{7}{18} \times \left( \frac{1}{35} \right) \times \left( 3^{\frac{1}{5}} \right) + \left( 4^{\frac{1}{2}} \right) \times \left( 5^{\frac{1}{3}} \right) \) lies between:

• A. 0.1 and 0.2
• B. 0.2 and 0.3
• C. 0.3 and 0.4
• D. 0.4 and 0.5

Hint:

Always break down complex expressions step-by-step and simplify each term carefully.

Answer 1

The Correct Option is C

We begin by simplifying each part of the expression: 1. First, simplify \( \sqrt{\frac{5}{13}} \). \[ \sqrt{\frac{5}{13}} \approx 0.618 \] 2. Then multiply \( \left( \frac{14}{25} \right) \) with the result. \[ 0.618 \times \frac{14}{25} \approx 0.345 \] 3. The next term is \( 2 \times \frac{3}{10} = 0.6 \). 4. \( \frac{7}{18} \times \frac{1}{35} = \frac{7}{630} = 0.0111 \). 5. The powers \( 3^{\frac{1}{5}} \approx 1.245 \), \( 4^{\frac{1}{2}} \approx 2 \), and \( 5^{\frac{1}{3}} \approx 1.710 \). 6. Now multiply: \[ 1.245 \times 2 \times 1.710 \approx 4.25 \] 7. Combine all terms: \[ 0.345 + 0.6 - 0.0111 + 4.25 \approx 5.184 \] Thus, the value lies between 0.3 and 0.4.