If `sqrt(3)=1.732`, then the value of `(9+2sqrt(3))/(sqrt(3))` is

Options

A. `7.169`
B. `7.196`
C. `5.198`
D. `2.296`

Answer

To solve the expression \((9 + 2\sqrt{3})/\sqrt{3}\), we can follow these steps:

### Step 1: Rewrite the Expression
We start with the expression:
\[ \frac{9 + 2\sqrt{3}}{\sqrt{3}} \]

### Step 2: Separate the Terms
We can separate the terms in the numerator:
\[ \frac{9}{\sqrt{3}} + \frac{2\sqrt{3}}{\sqrt{3}} \]

### Step 3: Simplify Each Term
Now, simplify each term:
1. For \(\frac{9}{\sqrt{3}}\), we can rationalize it by multiplying the numerator and the denominator by \(\sqrt{3}\):
\[ \frac{9\sqrt{3}}{3} = 3\sqrt{3} \]
2. For \(\frac{2\sqrt{3}}{\sqrt{3}}\), the \(\sqrt{3}\) cancels out:
\[ 2 \]

### Step 4: Combine the Results
Now, we combine the results from the two simplified terms:
\[ 3\sqrt{3} + 2 \]

### Step 5: Substitute the Value of \(\sqrt{3}\)
Given that \(\sqrt{3} = 1.732\), we substitute this value into the expression:
\[ 3(1.732) + 2 \]

### Step 6: Calculate the Value
Now, calculate \(3 \times 1.732\):
\[ 3 \times 1.732 = 5.196 \]
Now, add 2:
\[ 5.196 + 2 = 7.196 \]

### Final Answer
Thus, the value of \(\frac{9 + 2\sqrt{3}}{\sqrt{3}}\) is:
\[ \boxed{7.196} \]