$\sqrt{\frac{1.21 imes 0.9}{1.1 imes 0.11}}$ is equal to :

Question

$\sqrt{\frac{1.21 	imes 0.9}{1.1 	imes 0.11}}$ is equal to :

Accepted Answer

To determine why Option 2 is the correct answer for the expression $\sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}}$, we will evaluate the expression step by step.

1. **Simplify the Expression:**

The expression inside the square root is $\frac{1.21 \times 0.9}{1.1 \times 0.11}$.

- Calculate the numerator: $1.21 \times 0.9 = 1.089$.
   - Calculate the denominator: $1.1 \times 0.11 = 0.121$.

So, the expression becomes $\sqrt{\frac{1.089}{0.121}}$.

2. **Divide the Numerator by the Denominator:**

$\frac{1.089}{0.121} = 9$.

3. **Take the Square Root:**

$\sqrt{9} = 3$.

Thus, the value of the expression $\sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}}$ is 3, which corresponds to Option 2.

**Explanation for Other Options:**

- **Option 1 (2):** The value 2 is incorrect because the square root of 9 is 3, not 2.
  
- **Option 3 (9):** The value 9 is incorrect because it represents the result of the division before taking the square root, not the final result.

- **Option 4 (11):** The value 11 is incorrect because it does not relate to any part of the calculation process for this expression.

Therefore, based on the calculations, Option 2 is indeed the correct answer.