If `sqrt(5)=2.236`, then what is the value of `(sqrt(5))/(2)+(5)/(3sqrt(5))-sqrt(45)` ?

Options

A. `-8.571`
B. `-4.845`
C. `-2.987`
D. `-6.261`

Answer

To solve the expression \(\frac{\sqrt{5}}{2} + \frac{5}{3\sqrt{5}} - \sqrt{45}\), we will follow these steps:

### Step 1: Substitute the value of \(\sqrt{5}\)
Given that \(\sqrt{5} = 2.236\), we can substitute this value into the expression.

\[ \frac{\sqrt{5}}{2} + \frac{5}{3\sqrt{5}} - \sqrt{45} = \frac{2.236}{2} + \frac{5}{3 \cdot 2.236} - \sqrt{45} \]

### Step 2: Calculate \(\frac{2.236}{2}\)
Now, we calculate \(\frac{2.236}{2}\):

\[ \frac{2.236}{2} = 1.118 \]

### Step 3: Calculate \(\frac{5}{3 \cdot 2.236}\)
Next, we calculate \(\frac{5}{3 \cdot 2.236}\):

\[ 3 \cdot 2.236 = 6.708 \]
\[ \frac{5}{6.708} \approx 0.745 \]

### Step 4: Simplify \(\sqrt{45}\)
Now, we simplify \(\sqrt{45}\):

\[ \sqrt{45} = \sqrt{9 \cdot 5} = 3\sqrt{5} \]
Substituting \(\sqrt{5}\):

\[ 3\sqrt{5} = 3 \cdot 2.236 = 6.708 \]

### Step 5: Combine the values
Now we combine all the calculated values:

\[ 1.118 + 0.745 - 6.708 \]

### Step 6: Perform the final calculation
Now, we perform the final calculation:

\[ 1.118 + 0.745 = 1.863 \]
\[ 1.863 - 6.708 = -4.845 \]

### Final Answer
Thus, the value of the expression is approximately:

\[ \boxed{-4.845} \]