$$\sqrt{\frac{32.4}{12.1}} \times \sqrt{\frac{67.6}{14.9}} = ?$$​

Correct option is A

Given:

We are tasked to solve:

$$\sqrt{\frac{32.4}{12.1}} \times \sqrt{\frac{67.6}{14.9}}$$​

and match it with one of the given options.

Solution:

1. Simplify the expression:

$$\sqrt{\frac{32.4}{12.1}} \times \sqrt{\frac{67.6}{14.9}} = \sqrt{\frac{32.4 \times 67.6}{12.1 \times 14.9}}$$​

2. Calculate the numerator and denominator:

$$32.4 \times 67.6 = 2190.24$$​

$$12.1 \times 14.9 = 180.29$$​

3. Fraction under the square root:

$$\frac{2190.24}{180.29} = 12.15$$​

4. Take the square root of 12.15 :

$$\sqrt{12.15} \approx 3.636$$​

Verification with Options:

Convert options to decimal:

$$\text{Option A: } 3 \frac{7}{11} = 3 + \frac{7}{11} \approx 3.636$$​

$$\text{Option B: } 3 \frac{6}{11} = 3 + \frac{6}{11} \approx 3.545$$​

$$\text{Option C: } 2 \frac{8}{11} = 2 + \frac{8}{11} \approx 2.727$$​

$$\text{Option D: } 2 \frac{4}{11} = 2 + \frac{4}{11} \approx 2.364$$​

The closest match is Option A: $$3 \frac{7}{11}$$​ .

Final Answer:

Option A: $$3 \frac{7}{11}$$​