If `sqrt3 = 1. 732 ,` then find the value of `(9 + 2 sqrt3)/(sqrt3)`

Options

A. `7.169`
B. `7.196`
C. `5.198`
D. `7.296`

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

### Step 3: Simplify the second term
The second term simplifies as follows:
\[ \frac{2\sqrt{3}}{\sqrt{3}} = 2 \]
So, we have:
\[ \frac{9}{\sqrt{3}} + 2 \]

### Step 4: Rationalize the first term
To simplify \(\frac{9}{\sqrt{3}}\), we can multiply the numerator and the denominator by \(\sqrt{3}\):
\[ \frac{9\sqrt{3}}{3} = 3\sqrt{3} \]

### Step 5: Combine the terms
Now we can combine the terms:
\[ 3\sqrt{3} + 2 \]

### Step 6: Substitute the value of \(\sqrt{3}\)
Given that \(\sqrt{3} = 1.732\), we substitute this value into the expression:
\[ 3(1.732) + 2 \]

### Step 7: Calculate \(3 \times 1.732\)
Calculating this gives:
\[ 3 \times 1.732 = 5.196 \]

### Step 8: Add 2 to the result
Now we add 2:
\[ 5.196 + 2 = 7.196 \]

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

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