Given that: `sqrt(3)=1.732`, then `(sqrt(147) -1/4sqrt(48) -sqrt(75))` is equal to:

Options

A. `5.196`
B. `3.464`
C. `1.732`
D. `0.866`

Answer

To solve the expression \( \sqrt{147} - \frac{1}{4}\sqrt{48} - \sqrt{75} \) given that \( \sqrt{3} = 1.732 \), we will simplify each term step by step.

### Step 1: Simplify \( \sqrt{147} \)

We can factor \( 147 \) as follows:
\[ 147 = 49 \times 3 = 7^2 \times 3 \]
Thus, we can write:
\[ \sqrt{147} = \sqrt{7^2 \times 3} = 7\sqrt{3} \]

### Step 2: Simplify \( \sqrt{48} \)

Next, we simplify \( \sqrt{48} \):
\[ 48 = 16 \times 3 = 4^2 \times 3 \]
So, we have:
\[ \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \]

### Step 3: Simplify \( \sqrt{75} \)

Now, we simplify \( \sqrt{75} \):
\[ 75 = 25 \times 3 = 5^2 \times 3 \]
Thus, we can write:
\[ \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3} \]

### Step 4: Substitute back into the expression

Now we substitute these simplified forms back into the original expression:
\[ \sqrt{147} - \frac{1}{4}\sqrt{48} - \sqrt{75} = 7\sqrt{3} - \frac{1}{4}(4\sqrt{3}) - 5\sqrt{3} \]

### Step 5: Simplify the expression

Calculating \( \frac{1}{4}(4\sqrt{3}) \):
\[ \frac{1}{4}(4\sqrt{3}) = \sqrt{3} \]
Now, substituting this back into the expression:
\[ 7\sqrt{3} - \sqrt{3} - 5\sqrt{3} \]

Combine like terms:
\[ (7\sqrt{3} - \sqrt{3} - 5\sqrt{3}) = (7 - 1 - 5)\sqrt{3} = 1\sqrt{3} = \sqrt{3} \]

### Step 6: Final answer

Since we know \( \sqrt{3} = 1.732 \), the final answer is:
\[ \sqrt{147} - \frac{1}{4}\sqrt{48} - \sqrt{75} = 1.732 \]