>

> I have read that one can extract square roots utilizing Pascal's Triangle.

> Is anyone aware of the technique ?

>

Though it's not really on-topic for our list, I was hoping someone

knew a method... I was curious.

So here's the one I made up, feel free to better it.

One has a LARGE Pascal's triangle at hand, I take it? All I need is

the edge of it, though:

1

1

2 1

3 1

6 4 1

10 5 1

15 6 1

21 7 1

28 8 1

36 9 1

and so on...

I look at the 6,10,15,21,28,36,... diagonal, and pick the entry

closest to half of the number I want the square root of. So if I want

the square root of 70, I'll go with the 36. Then an approximation to the

square root is the average of the two numbers next to it in the next

diagonal over, (8 + 9)/2 = 8.5 . You want more accuracy? Simply multiply

your number by 100 (or 10,000 or 1,000,000 or ...). So to approximate

the square root of 7000, one looks for 3500, and finds:

1

1

82 1

83 1

3486 84 1

this gives 7000^.5 approximately equal to 83.5, and so

70^.5 is approximately equal to 8.35 ...