Question

The approximate value of $\sqrt[5]{533}$ is

• A. $2.0125$
• B. $2.1$
• C. $2.01$
• D. $3.258$

Answer 1

The correct option is A $2.0125$

Let $y=x^{1/5}$ where $x=32$ and $\Delta x=+1$

Now, $y=x^{1/5}$

Differentiating both sides wrt $x$,

$\frac{dy}{dx}=\frac{1}{5}{x}^{4/5}$

Using $\Delta y=\frac{dy}{dx}\Delta x$

$\Delta y=\frac{1}{5\left(x^{4/5}\right)}\Delta x$

Putting values,

$\Delta y=\frac{1}{5{\left(32\right)}^{4/5}}\left(1\right)$

Or, $\Delta y=\frac{1}{5\times 2^{5\times 4/5}}=0.0125$

We know,

$\Delta y=f(x+\Delta x)-f\left(x\right)$

Or, $\Delta y={(x+\Delta x)}^{1/5}-x^{1/5}$

$0.0125={(32+1)}^{1/5}-{(32+1)}^{1/5}$

Or, $0.125={33}^{1/5}-2^{5\times 1/5}$

Or, $2.0125={33}^{1/5}$

So, the approximate value of $5\sqrt{33}$ is $2.0125$