Without actual multiplication, find the squares of numbers 109 and 299.

109 can be written as (100 + 9).

⇒ 109² = (100 + 9)²

⇒ 109² = 100² + 2 × 100 × 9 + 9²

⇒ 109² = 10000 + 1800 + 81

∴ 109² = 11881

Therefore, square of 109 is 11881.

Similarly, 299 can be written as (300 − 1).

⇒ 299² = (300 − 1)²

⇒ 299² = (300)² − 2 × 300 × 1 + 1²

⇒ 299² = 90000 − 600 + 1

∴ 299² = 89401

Thus, the square of 299 is 89401.