Square and Cube numbers memory techniques

[bjoern.gumboldt (Бьёрн Гумбольдт / ब्योर्न गम्बोल्ट / 龚博 / 龔博宇)]

@Daniel_360

For squares, you should see some patterns in the data.

@chaitanya10 you can have a look here for the symmetry around 25.

How can I start mental calculating

Making progress with your squares, @Badr4sudan? I mentioned a few more shortcuts in my last reply, so here’s one. Let’s say you’ve made it up to 25² using the methods I’ve mentioned previously. There is a nice symmetry at 25 once you get there: [25-50] Use 25 as your base… Δ is the difference to 25. Say you want to square 28 in which case Δ = (28 - 25) = 3; so just take the square of (25 - Δ) = 22² = 484 and add to it (Δ x 100) = 300. The result is 484 + 300 = 784 Example: 32² Δ = 7 → …

…and once you’re at 50, you got the symmetry that @Daniel_360 already mentioned. That let’s you technically go all the way up to 100; however, I’d use the symmetry around 75 instead to make the calculation easier.

@Daniel_360

it’s pretty easy to memorize these directly using flashcards

Alternatively, you could build your PAO system in such a way that the O is a 3-digit number that represents the square of P. In mine, for example, I have “Kylie Minogue squeezing a LeMoN”

KM is 73 with a square of LMN which is 532_ and then you just append the unit digit squared (i.e., 3^2=9) to get 73^2=5,329 and that’d how you get the squares up to 100 without even calculating.