How to write a code which can decrease the range of the answer until we get the right value?

I want to write a code which can help me decrease the range of answer until i find it.For example,S=0:0.001:1;and i have to find a value which its square will be the 0.09,that is,x^2=0.09,and the answer is 0.3

Now,if every time i guess median,that is ,

First time i guess "0.5",but 0.5^2=0.25 ,not 0.09,so the range become S=0:0.001:0.5

Second time i guess "0.25",but 0.25^2=0.0625 ,not 0.09.so the range become S=0.25:0.001:0.5

Third time i guess (0.25+0.5)/2=0.375,but 0.375^2=0.140625 ,not 0.09,so the range become S=0.25:0.001:0.375

So the range will keep decreasing until i find the answer,and one of upper bound and lower bound of the range will be my wrong number which i just guess.but i don't know how to modify the code

My original code

%first time 
S=0:0.001:1;

x=0.5;

y=x^2;%not 0.09

%Second time 
S=0:0.001:x

q=0.25;

y=q^2;%not 0.09

%Third time 
S=q:0.001:x

w=0.375;

y=w^2%not 0.09

%Fourth time 
S=q:0.001:w %S=0.25:0.001:0.375

e=0.3125;

y=e^2 %not 0.09

%Fifth time 
S=e:0.001:w;

r=0.34;

y=r^2 %not 0.09
   
.
   
.
   
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until i found that y=0.09,so i can know the answer,however,this code is too long,i want to write a while or for loop to find the answer,does anyone know how to modify my code?

[darova]

Maybe you can find some more information if you will search for bisection method