`sqrt(169)/42xxsqrt(441)/26xx16/sqrt(225)=?`

Options

A. (4/5)
B. (9/15)
C. 57/29
D. none of these

Answer

To solve the expression \( \frac{\sqrt{169}}{42} \times \frac{\sqrt{441}}{26} \times \frac{16}{\sqrt{225}} \), we will simplify each square root and then perform the calculations step by step.

### Step 1: Calculate the square roots
- \( \sqrt{169} = 13 \)
- \( \sqrt{441} = 21 \)
- \( \sqrt{225} = 15 \)

### Step 2: Substitute the square roots back into the expression
Now, we can rewrite the expression with the calculated square roots:
\[ \frac{13}{42} \times \frac{21}{26} \times \frac{16}{15} \]

### Step 3: Multiply the fractions
We can multiply the numerators and the denominators:
\[ \frac{13 \times 21 \times 16}{42 \times 26 \times 15} \]

### Step 4: Simplify the expression
Now we will simplify the expression step by step.

1. **Calculate the numerator:**
- \( 13 \times 21 = 273 \)
- \( 273 \times 16 = 4368 \)

2. **Calculate the denominator:**
- \( 42 \times 26 = 1092 \)
- \( 1092 \times 15 = 16380 \)

So now we have:
\[ \frac{4368}{16380} \]

### Step 5: Simplify the fraction
To simplify \( \frac{4368}{16380} \), we can find the greatest common divisor (GCD) of 4368 and 16380.

- Dividing both the numerator and the denominator by their GCD (which is 12):
\[ \frac{4368 \div 12}{16380 \div 12} = \frac{364}{1365} \]

### Step 6: Further simplification
Now, we can check if \( \frac{364}{1365} \) can be simplified further. The GCD of 364 and 1365 is 1, so it cannot be simplified further.

### Step 7: Convert to mixed number if necessary
Since \( 364 \) and \( 1365 \) do not have any common factors, we can express it as a decimal or leave it as a fraction.

### Final Answer
Thus, the final answer is:
\[ \frac{364}{1365} \]