(√289/34) × (68/√1156) × (√961/62) = ?

Options

A. 1/2
B. 3/4
C. 5/6
D. 7/8

Answer

To solve the expression \((\sqrt{289}/34) \times (68/\sqrt{1156}) \times (\sqrt{961}/62)\), we will break it down step by step.

### Step 1: Calculate \(\sqrt{289}\)
\[ \sqrt{289} = 17 \]

### Step 2: Calculate \(\sqrt{1156}\)
\[ \sqrt{1156} = 34 \]

### Step 3: Calculate \(\sqrt{961}\)
\[ \sqrt{961} = 31 \]

### Step 4: Substitute the square roots back into the expression
Now we substitute the values we found into the original expression:
\[ \frac{17}{34} \times \frac{68}{34} \times \frac{31}{62} \]

### Step 5: Simplify \(\frac{17}{34}\)
\[ \frac{17}{34} = \frac{1}{2} \]

### Step 6: Simplify \(\frac{68}{34}\)
\[ \frac{68}{34} = 2 \]

### Step 7: Simplify \(\frac{31}{62}\)
\[ \frac{31}{62} = \frac{1}{2} \]

### Step 8: Combine the simplified fractions
Now we can combine these simplified fractions:
\[ \frac{1}{2} \times 2 \times \frac{1}{2} \]

### Step 9: Calculate the final result
\[ \frac{1}{2} \times 2 = 1 \]
\[ 1 \times \frac{1}{2} = \frac{1}{2} \]

Thus, the final answer is:
\[ \frac{1}{2} \]

### Summary of Steps:
1. Calculate \(\sqrt{289}\) = 17.
2. Calculate \(\sqrt{1156}\) = 34.
3. Calculate \(\sqrt{961}\) = 31.
4. Substitute back into the expression.
5. Simplify \(\frac{17}{34}\) to \(\frac{1}{2}\).
6. Simplify \(\frac{68}{34}\) to 2.
7. Simplify \(\frac{31}{62}\) to \(\frac{1}{2}\).
8. Combine the simplified fractions.
9. Calculate the final result.