The simplified value of `sqrt(0.25 xx 2.25)` is

Options

A. 0.075
B. 0.705
C. `0.750`
D. `7.500`

Answer

To simplify the expression \( \sqrt{0.25 \times 2.25} \), we can follow these steps:

### Step 1: Convert the decimals to fractions
We know that:
- \( 0.25 = \frac{25}{100} = \frac{1}{4} \)
- \( 2.25 = \frac{225}{100} = \frac{9}{4} \)

So, we can rewrite the expression as:
\[ \sqrt{0.25 \times 2.25} = \sqrt{\frac{1}{4} \times \frac{9}{4}} \]

### Step 2: Multiply the fractions
Now, we multiply the fractions:
\[ \frac{1}{4} \times \frac{9}{4} = \frac{1 \times 9}{4 \times 4} = \frac{9}{16} \]

### Step 3: Take the square root
Next, we take the square root of the resulting fraction:
\[ \sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4} \]

### Step 4: Convert to decimal
Now, we convert \( \frac{3}{4} \) to decimal:
\[ \frac{3}{4} = 0.75 \]

### Final Answer
Thus, the simplified value of \( \sqrt{0.25 \times 2.25} \) is:
\[ \boxed{0.75} \]