The square root of `((1)/(4))xx((1)/(49))-:((25)/(121))` is

Options

A. `(11)/(5)`
B. `(11)/(70)`
C. `(7)/(11)`
D. `(11)/(7)`

Answer

To solve the question, we need to find the square root of the expression \(\frac{1}{4} \times \frac{1}{49} \div \frac{25}{121}\).

### Step-by-Step Solution:

1. **Rewrite the Expression**:
We start with the expression:
\[ \sqrt{\frac{1}{4} \times \frac{1}{49} \div \frac{25}{121}} \]
We can rewrite the division as multiplication by the reciprocal:
\[ \sqrt{\frac{1}{4} \times \frac{1}{49} \times \frac{121}{25}} \]

2. **Multiply the Fractions**:
Now we multiply the fractions together:
\[ \frac{1 \times 1 \times 121}{4 \times 49 \times 25} \]
This simplifies to:
\[ \frac{121}{4900} \]

3. **Calculate the Square Root**:
Next, we find the square root of the fraction:
\[ \sqrt{\frac{121}{4900}} = \frac{\sqrt{121}}{\sqrt{4900}} \]

4. **Find the Square Roots**:
Now we calculate the square roots of the numerator and denominator:
- \(\sqrt{121} = 11\)
- \(\sqrt{4900} = 70\) (since \(70 \times 70 = 4900\))

5. **Final Result**:
Putting it all together, we have:
\[ \frac{11}{70} \]

Thus, the square root of \(\frac{1}{4} \times \frac{1}{49} \div \frac{25}{121}\) is \(\frac{11}{70}\).