Square roots and division of fractions: Find the square root of the expression (1/4) × (1/49) ÷ (25/121).

Introduction / Context:
This problem checks your ability to manipulate fractions inside a square root, including multiplication and division of rational numbers, and then simplifying the result before taking the square root. Such questions are common in aptitude tests to verify number sense and fraction skills.

Given Data / Assumptions:

• Expression: (1/4) × (1/49) ÷ (25/121)
• We must compute its value and then take the square root.

Concept / Approach:
Multiply fractions by multiplying numerators and denominators. Division by a fraction equals multiplication by its reciprocal. After simplification, take the square root of a simplified fraction a/b as sqrt(a)/sqrt(b), when a and b are non-negative rationals.

Step-by-Step Solution:
Compute product: (1/4) × (1/49) = 1/196.Divide by 25/121: (1/196) ÷ (25/121) = (1/196) × (121/25) = 121/4900.Now take the square root: sqrt(121/4900) = sqrt(121) / sqrt(4900) = 11 / 70.

Verification / Alternative check:
121 = 11^2 and 4900 = 70^2, so their ratio’s square root is simply 11/70. This confirms the arithmetic.

Why Other Options Are Wrong:
11/5, 7/11, and 11/7 are too large because the original value is less than 1; 5/11 does not match the precise simplification from the exact factor squares.

Common Pitfalls:
Students often forget that dividing by a fraction means multiplying by its reciprocal, or they take the square root term-by-term before simplifying the inner fraction, which can lead to errors.

Final Answer:
11/70