Question

The approximate value of $\sqrt[3]{3-0.99}$ is ______.

• A. $-0.9967$
• B. $0.9776$
• C. $-1.0033$
• D. $-1$

Answer 1

The correct option is A $-0.9967$

Let $b^3=-0.99$. Also, let us assume that $a=-1$ an $ϵ$ be a small correction factor such that $b=a+ϵ$.

Now, cubing both sides,

$b^3=a^3+3a^2ϵ+3a{ϵ}^2+{ϵ}^3$

$\therefore -0.99=-1+3ϵ-3{ϵ}^2+{ϵ}^3$

$\therefore {ϵ}^3-3{ϵ}^2+3ϵ-0.01=0$

Assuming that ${ϵ}^3<<{ϵ}^2<<ϵ$, we have

$3ϵ-0.01=0$

$\therefore ϵ=\frac{0.01}{3}$

$\therefore ϵ=0.0033$

$\therefore b=-1+0.0033=-0.9967$

This is the required solution.