Question

The value of 1.0004 to the power 1 by 2 using Binomial approximation is​

Answer 1

Given:

The given value is
`(1.0004)^{(1)/(2)}`.

To find:

The value of the given expression by using the Binomial approximation.

Step-by-step explanation:

We have,

`(1.0004)^{(1)/(2)}`

It can be written as:

`(1.0004)^{(1)/(2)}=(1+0.0004)^{(1)/(2)}`

`(1.0004)^{(1)/(2)}=1+(1)/(2)* 0.0004`
`[\because (1+x)^n=1+nx]`

`(1.0004)^{(1)/(2)}=1+0.0002`

`(1.0004)^{(1)/(2)}=1.0002`

Therefore, the approximate value of the given expression is 1.0002.