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Before embarking on a flight, the pilot of a private airplane plans the best route to the final

destination. Suppose the pilot determines one route covers a distance of \(\sqrt{500\) miles and another covers a distance of [tex] \sqrt{605} miles

Aa. Write an expression to represent the difference between the two distances of

each route. Then simplify the expression, keeping your answer in radical form.

Show all steps needed to write your answer in simplest form.


b.b. Use a calculator to change the answer to decimal form. Round the answer to the

nearest tenth. Using this decimal number, write a sentence to explain the

meaning of the answer in this situation.

Verified Answer :

Differ of these distances:

\(\sqrt{605} - \sqrt{500}\)

Simplify this distance:

\(\sqrt{605} - \sqrt{500} = \sqrt{121 \cdot 5} - \sqrt{100 \cdot 5}= \sqrt{121} \cdot \sqrt{5}-\sqrt{100} \cdot \sqrt{5}= \\ \\ = 11\sqrt{5}-10\sqrt{5}=\sqrt{5}\)

To a decimal form:  \(\sqrt{5} \approx 2.2\)

Meaning of the answer?  The answers  2.2  or \(\sqrt{5}\) is just very clear to  us  

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