Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 136

Question regards the Maths Is Fun Iteration page

On the iteration page it suggests using the following method to establish the square root of a number;

Example: to find a Square Root:
a) start with a guess
b) divide by the guess
c) add that to the guess
d) halve that for the new guess
e) now repeat (iterate) from step (b)

For the square root of 10, starting with a guess of 4 we get:

• 4
• 3.25
• 3.163
• 3.1623
etc...

My question. Regards, "b) divide by the guess" ; divide what by the guess?

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 164

Re: Question regards the Maths Is Fun Iteration page

a) 4
b) 10/4 = 2.5
c) 2.5 + 4 = 6.5
d) 6.5 / 2 = 3.25

a) 3.25
b) 10/3.25 = 3.077
c) 3.077 + 3.25 = 6.327
d) 6.327 / 2 = 3.163

...

Bob

Administrator

Registered: 2010-06-20

Posts: 10,172

Re: Question regards the Maths Is Fun Iteration page

The method works like this.

Suppose the number is N and G1 is your first guess.  Let G2 = N / G1

N = square root x square root. Also N = G1 x G2

If G1 is lower than the root then G2 must be higher; and if G1 is higher then G2 must be lower.

So, either way, root N lies between G1 and G2.

So, if you work out G3 = (G1+G2)/2 you get a number that is closer to the root than G1.

Using G3 as a 'better' guess leads to G4 and once again the true root must be between them.

So continuing the procedure leads to Gs that are closer and closer to the actual root.  When Gx and Gx+1 appear the same (ie differ by an amount so small as to be less that the displayed accuracy, you've got  a root that is close enough.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob