Question

The approximate value of $\sqrt[3]{28}$ is

• A. $3.0037$
• B. $3.037$
• C. $3.0086$
• D. $3.37$

Answer 1

The correct option is B

$3.037$

Explanation for the correct option:

Find the value of $\sqrt[3]{28}$.

Let $x=\sqrt[3]{28}$

$x={28}^{\frac{1}{3}}$

Taking log on both sides.

$$\begin{gathered} \Rightarrow \log x=\log {28}^{\frac{1}{3}} \\ \Rightarrow \log x=\frac{1}{3}\log 28\left[\log a^b=b\log a\right] \\ \Rightarrow \log x=\frac{1}{3}(1.4472) \\ \Rightarrow \log x=0.4824 \\ \Rightarrow x=\text{antilog}(0.4824) \\ \Rightarrow x\approx 3.037 \end{gathered}$$

Hence, option (B) is the correct answer.