`sqrt((0.49)/(0.25)) + sqrt((0.81)/(0.36))` is equal to :

Options

A. `7 (9)/(10)`
B. `2 (9)/(10)`
C. `(9)/(10)`
D. `9 (9)/(10)`

Answer

To solve the expression \( \sqrt{\frac{0.49}{0.25}} + \sqrt{\frac{0.81}{0.36}} \), we will simplify each term step by step.

### Step 1: Rewrite the fractions
We can rewrite the decimals as fractions:
\[ \sqrt{\frac{0.49}{0.25}} = \sqrt{\frac{49}{25}} \quad \text{and} \quad \sqrt{\frac{0.81}{0.36}} = \sqrt{\frac{81}{36}} \]

### Step 2: Simplify the square roots
Now, we can simplify the square roots:
\[ \sqrt{\frac{49}{25}} = \frac{\sqrt{49}}{\sqrt{25}} = \frac{7}{5} \]
\[ \sqrt{\frac{81}{36}} = \frac{\sqrt{81}}{\sqrt{36}} = \frac{9}{6} = \frac{3}{2} \]

### Step 3: Add the fractions
Now we need to add \( \frac{7}{5} \) and \( \frac{3}{2} \). To do this, we need a common denominator. The least common multiple (LCM) of 5 and 2 is 10.

Convert each fraction:
\[ \frac{7}{5} = \frac{7 \times 2}{5 \times 2} = \frac{14}{10} \]
\[ \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} \]

Now we can add them:
\[ \frac{14}{10} + \frac{15}{10} = \frac{14 + 15}{10} = \frac{29}{10} \]

### Step 4: Convert to mixed number
To convert \( \frac{29}{10} \) to a mixed number:
\[ 29 \div 10 = 2 \quad \text{with a remainder of } 9 \]
Thus, \( \frac{29}{10} = 2 \frac{9}{10} \).

### Final Answer
The final answer is:
\[ 2 \frac{9}{10} \]

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