Solve:(√7225−√1225) × (1⁄5)

Correct — A. Take each square root, subtract, then multiply by 1⁄5.

√7225 = 85, since 85² = 7225
√1225 = 35, since 35² = 1225

Subtract: 85 − 35 = 50
Multiply by 1⁄5: 50 × 1⁄5 = 10 → option (a)

Why the others are wrong

• (b)
  20 — 20 would need the bracket to equal 100. It is 85 − 35 = 50, and 50 × 1⁄5 = 10.
• (c)
  30 — 30 would need the bracket to equal 150. √7225 − √1225 = 85 − 35 = 50, so the product is 10.
• (d)
  40 — 40 would need the bracket to equal 200, four times the true 85 − 35 = 50.

A perfect square ending in 25 has a root ending in 5, and (10n + 5)² = 100 × n(n + 1) + 25.

So read the digits before 25:
7225 → 72 = 8 × 9, so √7225 = 85
1225 → 12 = 3 × 4, so √1225 = 35

A root does not split over subtraction: √7225 − √1225 is not √(7225 − 1225).

Key facts

• (10n + 5)² = 100 × n(n + 1) + 25, so 85² = 7225 and 35² = 1225.
• √a − √b is not equal to √(a − b).
• Multiplying by 1⁄5 is the same as dividing by 5.

Common traps

• Subtracting first and rooting after: √(7225 − 1225) = √6000 ≈ 77.46, which gives about 15.5, not an option.
• Guessing √1225 from its last digits alone. Every root ending in 5 squares to a number ending in 25, so check 35² = 1225 first.

No directly related past PYQ was found.