When `15 sqrt(15)` is divided by `3 sqrt(3)`, the quotient is

Options

A. `5 sqrt(3)`
B. `3 sqrt(5)`
C. `5 sqrt(5)`
D. `3 sqrt(3)`

Answer

To solve the problem of dividing \( 15 \sqrt{15} \) by \( 3 \sqrt{3} \), we will follow these steps:

### Step 1: Write the expression for division
We start with the expression:
\[ \frac{15 \sqrt{15}}{3 \sqrt{3}} \]

### Step 2: Simplify the coefficients
First, we can simplify the coefficients (the numbers outside the square roots):
\[ \frac{15}{3} = 5 \]
So, we can rewrite the expression as:
\[ 5 \cdot \frac{\sqrt{15}}{\sqrt{3}} \]

### Step 3: Simplify the square roots
Next, we simplify the square root part:
\[ \frac{\sqrt{15}}{\sqrt{3}} = \sqrt{\frac{15}{3}} = \sqrt{5} \]
Thus, the expression now becomes:
\[ 5 \cdot \sqrt{5} \]

### Step 4: Write the final answer
We can express the final answer as:
\[ 5 \sqrt{5} \]

### Conclusion
Therefore, the quotient of \( \frac{15 \sqrt{15}}{3 \sqrt{3}} \) is \( 5 \sqrt{5} \).

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