Question

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

Answer 1

Given:

The given value is $(1.0004)^{\frac{1}{2}}$.

To find:

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

Explanation:

We have,

$(1.0004)^{\frac{1}{2}}$

It can be written as:

$(1.0004)^{\frac{1}{2}}=(1+0.0004)^{\frac{1}{2}}$

$(1.0004)^{\frac{1}{2}}=1+\dfrac{1}{2}\times 0.0004$      $[\because (1+x)^n=1+nx]$

$(1.0004)^{\frac{1}{2}}=1+0.0002$

$(1.0004)^{\frac{1}{2}}=1.0002$

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