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# sir whats the value of under-root 2

Grade:Upto college level

## 2 Answers

Anurag Kishore
37 Points
11 years ago

Hi

As we know that 21/2 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) = x1/2

=> 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) = x1/2

=>   21/2 - 41/2 = -1/2

=> 21/2 = 2 - 1/2 =3/2 =1.5

Note differential give only approximate value and not exact

Thanks

swapnil sudhir
31 Points
11 years ago

the value of under root of 2 is 1.414

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