plz tell me irrational numbers between √2 and √3
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Answered by
2
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!
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!
Answered by
5
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 ^_^
---> 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 ^_^
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