Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, −√3) and (√5, 0)

Verified step by step guidance

1. Identify the coordinates of the two points: Point 1 is \((0, -\sqrt{3})\) and Point 2 is \((\sqrt{5}, 0)\).
2. Recall the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\): \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
3. Substitute the given coordinates into the distance formula: \(d = \sqrt{(\sqrt{5} - 0)^2 + (0 - (-\sqrt{3}))^2}\).
4. Simplify inside the square root: calculate \((\sqrt{5})^2\) and \((\sqrt{3})^2\), then add the results.
5. Express the distance in simplified radical form and then approximate the decimal value rounded to two decimal places.

Key Concepts

Distance Formula

The distance formula calculates the length between two points in the coordinate plane. It is derived from the Pythagorean theorem and given by d = √((x2 - x1)² + (y2 - y1)²). This formula helps find the straight-line distance between points (x1, y1) and (x2, y2).

Simplified Radical Form

Simplified radical form means expressing square roots in their simplest form by factoring out perfect squares. For example, √50 can be simplified to 5√2. This form is preferred before rounding to maintain exactness and clarity in answers.

Rounding to Decimal Places

Rounding involves approximating a number to a specified number of decimal places for simplicity. In this problem, answers are rounded to two decimal places, which means keeping two digits after the decimal point and adjusting the last digit based on the next digit's value.