The value of 52 × 3 ÷ 4 + √441 ÷ 7 × 3 + 5 – 32 ÷ 8 × 12 is :

Concept: When an expression mixes roots, multiplication, division, addition, and subtraction, BODMAS applies in this order — Brackets, Orders (powers and roots), then Division and Multiplication from left to right as they appear, and finally Addition and Subtraction from left to right. Division and multiplication share equal precedence, and so do addition and subtraction — within each pair, the operation written first (reading left to right) is evaluated first, neither one automatically before the other.

Application:

1. Evaluate the order (root) first: the square root of 441 is 21.

2. First division-multiplication group, left to right: 52 × 3 = 156, then 156 ÷ 4 = 39.

3. Second division-multiplication group, left to right: 21 ÷ 7 = 3, then 3 × 3 = 9.

4. Third division-multiplication group, left to right: 32 ÷ 8 = 4, then 4 × 12 = 48.

5. Substitute these results back into the expression: 39 + 9 + 5 – 48.

6. Add and subtract from left to right: 39 + 9 = 48, then 48 + 5 = 53, and finally 53 – 48 = 5.

Cross-check: Grouping the additive terms independently gives the same result — adding all the positive contributions first (39 + 9 + 5 = 53) and then subtracting the one negative contribution (53 – 48 = 5) confirms the value without changing the left-to-right order within any group.

So the value of the expression is 5.