Square and Cube numbers memory techniques

[bjoern.gumboldt]

@chaitanya10

What memory techniques he could have used to learn these concepts.

That depends… you can either use memory techniques or simply concepts from mental math.

@chaitanya10

When he as about square of 87 and 76 he was able to tell in a jiffy.

Unfortunately, “a jiffy” is not a very quantitative way of referring to things… let’s take the mental math approach first for the 76^2 above.

Squares ending in 0 or 5 are super easy to calculate. Pick 75; since it’s closer than 80. To calculate a two digit number a|b (in this case 7|5), multiply a(a+1) for the left hand side (here 7*8) and square b for the right hand side (always 25). To get from 75^2=5,625 to 76^2, you just double the number you squared (here 75*2=150 and add it on top, plus an additional 1 for 5,625+150+1=5,776

For a bit more in-depth about this approach have a look here…

How to calculate squares quickly

It’s a shame we only have a like button, because this post is 5 out of 5 stars! The only way this could be better (five-and-a-half stars) is if you’d have called if squares with binomial formulas. It’s pretty clear that you are using the first and second formula when adding and subtracting, but even the numbers ending in 5 are done with the third: \color{blue}{(a+b)^2=a^2+2ab+b^2} \color{blue}{(a-b)^2=a^2-2ab+b^2} \color{blue}{(a+b)*(a-b)=a^2-b^2} For those interested, the nice thing he…

@chaitanya10

Also when he was given last 3 digits of a cube number, he completed remaining 3 digits and he told its cube root immediately.

I don’t understand what you mean by “completed remaining 3 digits” but cube roots are easier than square roots. Just search here on the forum or google “Vedic math cube roots”. Both your question have been explained before on here, so you shouldn’t have a problem finding the information using the search function.