solve (√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 simplify each term step by step.

### Step 1: Simplify \(\sqrt{289}\)
\[ \sqrt{289} = 17 \]
So, we can rewrite the first term:
\[ \frac{\sqrt{289}}{34} = \frac{17}{34} \]

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

### Step 3: Simplify \(\sqrt{1156}\)
\[ \sqrt{1156} = 34 \]
So, we can rewrite the second term:
\[ \frac{68}{\sqrt{1156}} = \frac{68}{34} \]

### Step 4: Simplify \(\frac{68}{34}\)
\[ \frac{68}{34} = 2 \]

### Step 5: Simplify \(\sqrt{961}\)
\[ \sqrt{961} = 31 \]
So, we can rewrite the third term:
\[ \frac{\sqrt{961}}{62} = \frac{31}{62} \]

### Step 6: Simplify \(\frac{31}{62}\)
\[ \frac{31}{62} = \frac{1}{2} \]

### Step 7: Combine all terms
Now we can combine all simplified terms:
\[ \left(\frac{1}{2}\right) \times 2 \times \left(\frac{1}{2}\right) \]

### Step 8: Calculate the final result
\[ \frac{1}{2} \times 2 = 1 \]
\[ 1 \times \frac{1}{2} = \frac{1}{2} \]

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