If a*b*c = `sqrt((a+2)(b+3))/(c+1)`, then the value of (6*15*3) is :

Options

A. 6
B. 3
C. 4
D. can't be determined

Answer

To solve the problem, we need to evaluate the expression \(6 * 15 * 3\) using the given operation defined as:

\[ a * b * c = \sqrt{\frac{(a + 2)(b + 3)}{(c + 1)}} \]

### Step-by-step Solution:

1. **Identify the values of a, b, and c**:
- Here, \(a = 6\), \(b = 15\), and \(c = 3\).

2. **Substitute the values into the formula**:
- We substitute \(a\), \(b\), and \(c\) into the expression:
\[ 6 * 15 * 3 = \sqrt{\frac{(6 + 2)(15 + 3)}{(3 + 1)}} \]

3. **Calculate the values inside the parentheses**:
- Calculate \(6 + 2\):
\[ 6 + 2 = 8 \]
- Calculate \(15 + 3\):
\[ 15 + 3 = 18 \]
- Calculate \(3 + 1\):
\[ 3 + 1 = 4 \]

4. **Substitute these values back into the expression**:
- Now, we can rewrite the expression:
\[ 6 * 15 * 3 = \sqrt{\frac{(8)(18)}{4}} \]

5. **Calculate the numerator**:
- Multiply \(8\) and \(18\):
\[ 8 \times 18 = 144 \]

6. **Divide by the denominator**:
- Now divide \(144\) by \(4\):
\[ \frac{144}{4} = 36 \]

7. **Take the square root**:
- Finally, take the square root of \(36\):
\[ \sqrt{36} = 6 \]

### Final Result:
Thus, the value of \(6 * 15 * 3\) is \(6\).

---