sir whats the value of under-root 2

Hi

As we know that 2^1/2 is irrational so its value is non recurring and is equal to 1.414213562..........

But if you want value by differential approximation proceed as follows

Let,

f(x) = x^1/2

=> f^/(x) = 1/2 (x^-1/2)

Let x = 4      and       $x = -2

Now by differential approximation

f(x+$x) - f(x) = f^/(x) . $x

=>  f(4 - 2) - f(4) = 1/2(4^-1/2) . (-2)

=> f(2) - f(4) = -1/2

but from above f(x) = x^1/2

=>   2^1/2 - 4^1/2 = -1/2

=> 2^1/2 = 2 - 1/2 =3/2 =1.5

Note differential give only approximate value and not exact

Thanks

the value of under root of 2 is 1.414