Question

Give an approximation of underroot(3) correct to hundredths. (Round to two decimal places as needed.)

Answer 1

Answer: 1.75

Step-by-step explanation:

To find the value of $\sqrt{3}$

$\text{Let , }y=\sqrt{x}$

$\text{And Let x = 4 and }\Delta x=-1$

Now,

$\Delta y=\sqrt{x+\Delta x}-\sqrt{x}\\\\=\sqrt{3}-\sqrt{4}=\sqrt{3}-2\\\\\Rightarrow\ \sqrt{3}=\Delta y+2$

Since dy is approximately equals to $\Delta y$ then ,

$dy=\dfrac{dy}{dx}\Delta x\\\\=\dfrac{1}{2\sqrt{x}}\times(-1)=\dfrac{1}{2\sqrt{4}}\times(-1)=-0.25$

Thus , the approximate value of  $\sqrt{3}=-0.25+2=1.75$