Question

plz tell me irrational numbers between √2 and √3

Answer 1

Hey there!

As we all know,

√2 = 1.414  
√3 = 1.732

So, rational number between √2 and √3 are 
1.432, 1.563, 1.576, 1.657, 1.711 & many more (Infinite)

Cheers!

Answer 2

Heya User,

---> Let's take a line --> " Number line "

--> Obviously, if we have to cut it into two equal halves, we'll choose the '0' as the point of intersection... But why :-> coz the avg. any number 'n' on +ve no. line plus the mirror of that no. '-n' is 0...

Now, talking of average, Average of any two no.s will always lie between the two in the number line...

--> However, since we're talking of points and decimals here, the decimals, 0.1, 0.01, 0.001, 0.0001, ... has no end =_= ...

So, sorry for the above introduction... ^_^ Just avoid it..

--> Since we have to find irrational no.s b/w √2 and √3, we can't afford to let a pattern occur between the decimals.. more likely.. no pattern...

--> Let 'n' be such a no. such that :->
---> √2 < n < √3 

Even after squaring, the inequality will retain themselves :->
---> 2 < n² < 3

Umm.. n² = 2.1, 2.2, 2.3, 2.4, 2.5, 2.6 ..... or further, 2.01, 2.001, 2.0001, etc. also suffices...

---> Considering an under root irrational, √2.1 , √2.2 etc. would get you perfect marks ^_^

However, for an unbalanced soul { teachers }, one can frame a soln. such as :->

--> Since, √2 < 1.42 < n < 1.72 < √3 ,
--> One can find answers like :->

--> 1.4301001000100001000001... || 1.536284629201863527392... 
Or any such answer which doesn't show a pattern for repetition..

Hope you're satisfied with the Answer ^_^