Study guides › Level 6 · Master

Squaring numbers that end in 5

Level 6 · Master · for questions like “65² = ?”

💡 The idea

Every number ending in 5 squares the same way: the answer always ends in 25, and the front comes from a quick multiplication.

🪜 The steps

1. Take the digits before the 5 (for 65, that's 6).
2. Multiply that by the next number up (6 × 7 = 42).
3. Write 25 after it: 4225.

✏️ Worked examples

1. 65²: 6 × 7 = 42, so the answer is 4,225.

2. 115²: 11 × 12 = 132, so the answer is 13,225.

⚠️ Watch out

• Multiply by the next number up, not by itself: for 35², it's 3 × 4, not 3 × 3.
• Always 25 at the end, never 5.

🤔 Why it works

(10n + 5)² = 100n² + 100n + 25 = 100 × n(n + 1) + 25.

🎯 Try these

1. 35²
2. 85²
3. 105²

Answers: 1) 1,225 2) 7,225 3) 11,025

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.