# How can I start mental calculating

**URL:** https://forum.artofmemory.com/t/how-can-i-start-mental-calculating/34895
**Category:** Mental Calculation, Mathematics, and Puzzles
**Created:** [December 25, 2018, 1:49pm UTC](https://forum.artofmemory.com/t/how-can-i-start-mental-calculating/34895 "2018-12-25T13:49:30Z")
**Posts on this page:** 1
**Showing post:** 34

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### Author: ![bjoern.gumboldt](https://forum.artofmemory.com/user_avatar/forum.artofmemory.com/bjoern.gumboldt/32/16747_2.png) [@bjoern.gumboldt](https://forum.artofmemory.com/u/bjoern.gumboldt)
#### Post date: [January 27, 2019, 1:49pm UTC](https://forum.artofmemory.com/t/how-can-i-start-mental-calculating/34895/34 "2019-01-27T13:49:05Z")

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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](https://forum.artofmemory.com/uploads/default/original/2X/7/7bd9ef36ff895250bd8509669d34b18676322c54.png)

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  
→ (25 - Δ)² = 18² = 324  
→ add Δ x 100 = 700 to 324  
and you get 1024

So once you know the squares up to 25, you automatically know the squares up to 50 by reusing the squares from 1 to 25 and performing basic addition. Of course, still use case 0 and case 1 for 30, 35, 40, 45, and 50.

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