Given:
The given value is [tex](1.0004)^{\frac{1}{2}}[/tex].
To find:
The value of the given expression by using the Binomial approximation.
Explanation:
We have,
[tex](1.0004)^{\frac{1}{2}}[/tex]
It can be written as:
[tex](1.0004)^{\frac{1}{2}}=(1+0.0004)^{\frac{1}{2}}[/tex]
[tex](1.0004)^{\frac{1}{2}}=1+\dfrac{1}{2}\times 0.0004[/tex] [tex][\because (1+x)^n=1+nx][/tex]
[tex](1.0004)^{\frac{1}{2}}=1+0.0002[/tex]
[tex](1.0004)^{\frac{1}{2}}=1.0002[/tex]
Therefore, the approximate value of the given expression is 1.0002.
