`10sqrt(12) -: 2sqrt(3)`

Options

A. 5
B. 10
C. 40
D. 20

Answer

To solve the expression \( \frac{10\sqrt{12}}{2\sqrt{3}} \), we can follow these steps:

### Step 1: Simplify the expression
We start with the expression:
\[ \frac{10\sqrt{12}}{2\sqrt{3}} \]

### Step 2: Separate the constants and the square roots
We can rewrite the expression by separating the constants (10 and 2) from the square roots:
\[ = \frac{10}{2} \cdot \frac{\sqrt{12}}{\sqrt{3}} \]

### Step 3: Simplify the constants
Now, simplify \( \frac{10}{2} \):
\[ = 5 \cdot \frac{\sqrt{12}}{\sqrt{3}} \]

### Step 4: Simplify the square roots
Next, we can simplify \( \frac{\sqrt{12}}{\sqrt{3}} \) using the property of square roots:
\[ = 5 \cdot \sqrt{\frac{12}{3}} \]
Calculating \( \frac{12}{3} \):
\[ = 5 \cdot \sqrt{4} \]

### Step 5: Calculate the square root
Now, we know that \( \sqrt{4} = 2 \):
\[ = 5 \cdot 2 \]

### Step 6: Final multiplication
Finally, multiply the constants:
\[ = 10 \]

Thus, the final answer is:
\[ \boxed{10} \]

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