While mapping a landing zone above the Moon, Emek and Luna discovered four loose distance labels: 2.6, 13/5, sqrt(49), and sqrt(30) kilometers. The map separated routes into rational and irrational distance categories, so they had to classify each label before choosing a safe path. Luna noticed that 2.6 and 13/5 represented the same rational value. Emek simplified sqrt(49) to 7, making it rational as well. The remaining label, sqrt(30), was different because 30 is not a perfect square, so its square root is irrational. Two possible landing routes then appeared: one marked 13/5 kilometers and another marked sqrt(30) kilometers. Since sqrt(30) lies between sqrt(25) and sqrt(36), they knew its distance was between 5 and 6 kilometers. The 13/5-kilometer route was only 2.6 kilometers, so they selected the shorter safe route. With the labels restored, the landing map was complete.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Consider whether 30 and 35 are perfect squares, then compare the numbers inside their square roots.
A new lunar route is labeled sqrt(35) kilometers. Which statement best compares this route with the sqrt(30)-kilometer route from the story?
Both distances are rational, and sqrt(35) is longer.Both distances are irrational, and sqrt(35) is longer.Both distances are irrational, and sqrt(30) is longer.sqrt(35) is rational, while sqrt(30) is irrational.
Correct! Neither 30 nor 35 is a perfect square, and sqrt(35) is greater than sqrt(30).
Not quite. First classify both square roots, then compare their values.
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Hint
The story identifies three original labels as rational. Classify each of the three new labels and add the rational ones to that count.
The map adds three new distance labels: sqrt(64), sqrt(20), and 4.5 kilometers. Including the four original labels 2.6, 13/5, sqrt(49), and sqrt(30), how many of the seven labels are rational?
Correct! Five of the seven distance labels are rational.
Check whether each new label can be written as a ratio of integers, then combine that result with the original classifications.
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Hint
Rewrite or estimate each distance: the story gives 13/5 = 2.6 and places sqrt(30) between 5 and 6.
A third possible landing route is labeled sqrt(9) kilometers. Which ordering correctly lists the three route distances 13/5, sqrt(9), and sqrt(30) from shortest to longest?
sqrt(9), 13/5, sqrt(30)sqrt(30), sqrt(9), 13/513/5, sqrt(30), sqrt(9)13/5, sqrt(9), sqrt(30)
Correct! The distances increase from 2.6 to 3 to a value between 5 and 6.
Not quite. Compare 13/5 = 2.6, sqrt(9) = 3, and the story's estimate for sqrt(30).
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Ay Haritasını Onarmak
TR
ARC_G08_NUM_02_STORY_02
Ay Haritasını Onarmak
Repairing the Lunar Map
EN
ARC_G08_NUM_02_STORY_02
Repairing the Lunar Map