### Math trick and its proof: square a number ending in 5

I will be hosting the blog carnival Math Teachers at Play next week. (You can send in submissions here.)

One submission I got about various multiplication tricks or shortcuts got me inspired to write a proof of the particular trick.

You could definitely use this in algebra class. First explain the shortcut or trick itself. Then ask students to prove it, or to explain WHY it works, using algebra.

You could also explain this to younger students as an additional "neat trick" and let them explore and play with it.

THE "TRICK"

If a number ends in 5, then its square can be calculated using this "trick" (I like to call it a shortcut because there's nothing magic about it):

Let's say we have 75 × 75 => Go 7 × 8 = 56. Then tag 25 (or 5 × 5) into that. You get 5625.

Let's say we have 35 × 35 => Go 3 × 4 = 12. Then tag 25 into that. You get 1225.

Let's say we have 115 × 115 => Go 11 × 12 = 132. Then tag 25 into that. You get 13,225.

Let's say w…

One submission I got about various multiplication tricks or shortcuts got me inspired to write a proof of the particular trick.

You could definitely use this in algebra class. First explain the shortcut or trick itself. Then ask students to prove it, or to explain WHY it works, using algebra.

You could also explain this to younger students as an additional "neat trick" and let them explore and play with it.

THE "TRICK"

If a number ends in 5, then its square can be calculated using this "trick" (I like to call it a shortcut because there's nothing magic about it):

Let's say we have 75 × 75 => Go 7 × 8 = 56. Then tag 25 (or 5 × 5) into that. You get 5625.

Let's say we have 35 × 35 => Go 3 × 4 = 12. Then tag 25 into that. You get 1225.

Let's say we have 115 × 115 => Go 11 × 12 = 132. Then tag 25 into that. You get 13,225.

Let's say w…