If 8 × 5 means 8 – 52 and 9 $ 3 means √9 + 32, then what is the value of 25 ×…

Concept: In symbol-substitution (operator-renaming) reasoning questions, an unfamiliar sign such as '×' or '$' is redefined by a worked example. Read the example as a general rule linking the two numbers involved, then apply that same rule — with the actual numbers from the question — strictly in the order the expression is written.

Application:

1. From '8 × 5 means 8 – 52', the rule for '×' is: p × q = p – q2.

2. From '9 $ 3 means √9 + 32', the rule for '$' is: r $ s = √r + s2.

3. Apply '×' first: 25 × 3 = 25 – 32 = 25 – 9 = 16.

4. Apply '$' to that result and 6: 16 $ 6 = √16 + 62 = 4 + 36 = 40.

Cross-check: 32 = 9 and 25 – 9 = 16 is a perfect square, so √16 is exactly 4; adding 62 = 36 gives 4 + 36 = 40, with no fractional or negative value appearing at any step — confirming the substitutions were applied correctly and in the right order.

The value of 25 × 3 $ 6 is 40.