Question

How to find the square of 45 containing 5 in the unit's place ?

Answer 1

Answer : 2025

General formula for sqaure of Number of type N5

(N5)² = N*(N+1)*100 + 25

(45)² = 4*5*100 + 25 = 2025

Proof

N5 = 10*N +5

(N5)² = (10N +5) * (10*N +5)

(N5)² = 100N² + 50N +50N +25

(N5)² = 100N² + 100N +25

(N5)² = 100*(N² + N)+25

(N5)² = N*(N+1)*100 + 25

Squares Ending in 5

Give me any 2 digit number that ends in 5, and I'll square it in my head! 452 = 2025 852 = 7225, etc. There's a quick way to do this: if the first digit is N and the second digit is 5, then the last 2 digits of the answer will be 25, and the preceding digits will be N*(N+1). Presentation Suggestions: After telling the trick, have students see how fast they can square such numbers in their head, but doing several examples. The Math Behind the Fact: You may wish to assign the proof as a fun homework exercise: multiply (10N+5)(10N+5) and interpret! The trick works for larger numbers, too, although it may be harder to do this in your head.