What will come in place of the question mark ‘?’ in the following question?

Concept: Simplifying a mixed expression with roots and fractions follows two rules — the square root of a perfect-square fraction, √(a²/b²) = a/b for positive a, b — and the standard order of operations (BODMAS): resolve roots and products before addition or subtraction, then combine any remaining fractions over their least common denominator (LCD).

1. Simplify the square root: since 169 = 132 and 225 = 152, √(169/225) = 13/15.

2. Multiply: (24/13) × (13/15) — the 13s cancel, leaving 24/15, which reduces to 8/5.

3. The expression now reads 8/5 + 14/9 − 1/3. The least common denominator of 5, 9 and 3 is 45.

4. Convert each fraction to forty-fifths: 8/5 = 72/45, 14/9 = 70/45, 1/3 = 15/45.

5. Combine: 72/45 + 70/45 − 15/45 = 127/45.

6. Convert to a mixed number: 127 ÷ 45 = 2 remainder 37, so 127/45 = 2 37/45.

Cross-check with decimals: 24/13 ≈ 1.846, √(169/225) ≈ 0.867, so the product ≈ 1.6; adding 14/9 ≈ 1.556 and subtracting 1/3 ≈ 0.333 gives ≈ 2.822, which matches 2 37/45 ≈ 2.822.

So the value that replaces the question mark is 2 37/45.