The simplified value of `sqrt((1.21 xx 0.9 )/(1.1 xx 0.11 ))`is -

Options

A. 2
B. 3
C. 9
D. 11

Answer

To simplify the expression \( \sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}} \]

### Step 2: Eliminate decimals
To eliminate the decimals, we can multiply both the numerator and the denominator by 1000 (to shift the decimal places). This gives us:
\[ \sqrt{\frac{1.21 \times 0.9 \times 1000}{1.1 \times 0.11 \times 1000}} = \sqrt{\frac{1210 \times 9}{110 \times 11}} \]

### Step 3: Calculate the numerator and denominator
Now we calculate the values:
- Numerator: \( 1210 \times 9 = 10890 \)
- Denominator: \( 110 \times 11 = 1210 \)

So, we have:
\[ \sqrt{\frac{10890}{1210}} \]

### Step 4: Simplify the fraction
Next, we simplify \( \frac{10890}{1210} \):
\[ \frac{10890 \div 1210}{1210 \div 1210} = \frac{9}{1} = 9 \]

### Step 5: Take the square root
Now we take the square root:
\[ \sqrt{9} = 3 \]

### Final Answer
Thus, the simplified value of \( \sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}} \) is:
\[ \boxed{3} \]