Question

The value of $\sqrt{24.99}$ is

• A. 5.001
• B. 4.999
• C. 4.897
• D. 4.899

Answer 1

Answer: (B)

$\sqrt{24.99}$
$\Delta y=f\left(x+\Delta x\right)-f\left(x\right)$
Take $f\left(x\right)=\sqrt{x}$
$Letx=25$
$\Delta x=-0.01$
$\therefore f\left(24.99\right)=\sqrt{25}+\Delta y$
$\approx 5-0.001$
$\approx 4.999$
$\Delta y\approx \frac{dy}{dx}\times \Delta x$
$\approx \frac{1}{2\sqrt{x}}\times -0.01$
$\approx -\frac{0.01}{10}$