Question

find the distance between the pair of points $(0,-\sqrt{3})$ and $(\sqrt{5},0)$. if necessary, express the answer in simplified radical form and then round to two decimal places.
the distance between the given points is $\square$ units.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 0,y_1=-\sqrt{3},x_2=\sqrt{5},y_2 = 0\).

Step2: Substitute the values into the formula

Substitute the values into the formula:

$$
LATEXBLOCK0
$$

Step3: Simplify the expression

Since \((\sqrt{a})^2=a\) for \(a\geq0\), we have \((\sqrt{5})^2 = 5\) and \((\sqrt{3})^2=3\). Then \(d=\sqrt{5 + 3}=\sqrt{8}\). Simplify \(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\).

Answer:

\(2\sqrt{2}\)