Can you explain this? 5 to the power of 2 trick...

Added: 2026-05-17

[00:00:00]5 squared is 25. 5 squared is 25. 5 squared is 25 and you notice there is a pattern. Now, what about these other numbers? Well, 1 * the next number 2 is 2. 2 * the next number 3 is 6. 3 * the next number 4 is 12 and this keeps happening. But, why?

[00:00:22]Let's take a look. Every single one of these numbers on the left side of the equality can be written as 10 n + 5. 5 is the ones digit and 10 n will be tens digit on. All of these are squared. When we distribute completely, we get 100 n squared + 100 n + 25. Notice these two terms right here. They have a common factor of 100 n leaving just n + 1 and plus that 25. That 25 is the only number in the tens and ones digit because n * n + 1 will always start or end in the hundreds place. And notice how n * n + 1 is a number * the next consecutive number. Follow for more math lessons like this and if you really enjoyed this, I teach like this in my courses.

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