Question

Approximate value of $(1.04{)}^{\frac{1}{4}}$ is

• A. $1.02$
• B. $1.04$
• C. $1.01$
• D. $1.08$

Answer 1

Answer: (C)

$1.01$

$\text{Approximate value of}(1.04{)}^{1/4}$

$\begin{array}{c}\text{for any quantity of form}(1+x{)}^n\text{where}x\text{is}\\ \text{a very small number with respect to}1\text{; whure}n\in R\text{.}\\ \text{So we can write by Binomial expansion.}\end{array}$

$(1+x{)}^n\approx 1+n\cdot x$

$\begin{array}{c}\text{So in ques}\text{we have}(1.04{)}^{1/4}=(1+0.04{)}^{1/4}\\ \text{So approximate value}=1+\frac{1}{4}\cdot \left(0.04\right)\\ =1+0.01=1.01\end{array}$