Squaring Numbers Ending in 5 - Lightning Fast!

Ever need to square a number like 35 or 75 quickly? Forget long multiplication! There's a super-speedy trick to amaze your friends and ace tests!

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

The Trick

To square any number that ends in 5, follow these two steps: 1. Take the digit(s) before the 5 (let's call it $N$). 2. Multiply $N$ by the next consecutive integer ($N+1$). 3. Append $25$ to the result of step 2. That's it! For example, for $A5^2$, the answer is $(A \times (A+1))$ followed by $25$. Why it works: A number ending in 5 can be written as $(10N+5)$. Squaring this gives $(10N+5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. The $100N(N+1)$ means $N(N+1)$ is in the hundreds place, and $25$ is added.

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.