Squaring a number — the fast way

There are two core techniques. First, for numbers ending in 5: multiply the tens digit by the next number up and append 25: 35² = 3×4=12 plus 25 → 1225. Second, for any number: a² = (a+b)(a−b) + b², i.e. shift the number to a convenient round one. 48² = 50×46 + 2² = 2300+4 = 2304; 62² = 60×64 + 2² = 3840+4 = 3844.

Squares come up constantly in geometry (areas), the Pythagorean theorem and algebra. The shifting trick is really the difference-of-squares formula — by using it mentally, a child starts handling algebraic identities long before the formal algebra course.

• Age: 10-11 and up.
• Common mistake: forgetting to add b² back after the shift — 48² is not just 50×46.
• Practice tip: memorise the squares from 1 to 25 as anchors — larger squares are computed through them.