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Chapter 2: Problem 16

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(2 \sqrt{3}, \sqrt{6}) \text { and }(-\sqrt{3}, 5 \sqrt{6})$$

Short Answer

Expert verified
The distance is approximately 11.09 or \(\sqrt{123}\) in simplified radical form.

Step by step solution

01

Identify coordinates

Identify coordinates of the two points. For the point (2 \sqrt{3}, \sqrt{6}), the coordinates are x1 = 2 \sqrt{3} and y1 = \sqrt{6}. For the point (-\sqrt{3}, 5\sqrt{6}), the coordinates are x2 = -\sqrt{3} and y2 = 5\sqrt{6}.
02

Employ the Distance Formula

Substitute these coordinates into the distance formula \sqrt{(x2-x1)^2+(y2-y1)^2}. This yields the equation \sqrt{(-\sqrt{3}-2\sqrt{3})^2+(5\sqrt{6}-\sqrt{6})^2}.
03

Simplify

Next, simplify the equation. \sqrt{(-3\sqrt{3})^2+(4\sqrt{6})^2} results in \sqrt{27+96}.
04

Calculate distance

Compute the square root to get the final distance. \sqrt{123} is an irrational number, so it can be left as is, or approximated to a decimal. The final distance is then approximately 11.09 when rounded to two decimal places.

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