Super-Speed Squaring (Ends in 5!)

Ever wish you could square big numbers like 35, 75, or even 105 in seconds, WITHOUT a calculator? Your wish just came true!

Subject: mental-calculation • Classes: 6–12 • Difficulty: intermediate

The Trick

To square any number ending in 5, let's call the number $N5$ (where $N$ is the digit(s) before the 5), follow these two simple steps: 1. Take the 'tens' digit (or the number $N$). Multiply it by the next consecutive integer, $(N+1)$. 2. Append '25' to the result of step 1. That's your answer! Why it works: Any number ending in 5 can be written as $(10N + 5)$. Squaring this gives $(10N+5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. This algebraic expansion clearly shows that the result is $N(N+1)$ followed by 25.

Study More with GyanAI

GyanAI is a free AI tutor for CBSE students. Ask any question for an instant step-by-step answer. Try GyanAI free.