At a lunar research base, Emek and Tara tried to combine measurements from two exploration rovers. One rover had classified each value into only one number set, causing conflicts in the database. It labeled sqrt(49) only as irrational because it contained a square root symbol. Tara simplified it to 7 and explained that 7 is natural, integer, rational, and real. Another measurement, -4, was labeled only as an integer. Emek pointed out that -4 can also be written as -4/1, so it is rational and real. They checked 0.625 and rewrote it as 5/8, confirming that it was rational, while sqrt(10) remained irrational because 10 is not a perfect square. Emek and Tara used the nesting of the number sets to correct every entry instead of choosing overly narrow categories. Once the classifications matched, the rover records combined successfully into one reliable database for future lunar missions.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Check whether 49 is a perfect square before classifying its square root.
The rover labeled sqrt(49) as irrational because it contained a square root symbol. Which explanation best identifies the rover's mistake?
Every number containing a square root symbol is rational.Square roots should always be classified as integers.The value must be simplified first; sqrt(49) = 7, which is natural, integer, rational, and real.The value is irrational because 49 is an odd number.
Correct. The square root symbol alone does not make a number irrational; sqrt(49) simplifies to 7.
Simplify sqrt(49) before deciding which number sets contain its value.
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Hint
Simplify or rewrite each value when possible, then decide whether it can be written as a fraction of integers.
For the four rover values sqrt(49), -4, 0.625, and sqrt(10), how many are rational numbers?
Correct. Three of the four rover values are rational.
Check sqrt(49), -4, and 0.625 carefully before deciding whether each can be written as a fraction of integers.
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Hint
Remember that a rational number can be written as a fraction of two integers with a nonzero denominator.
Another rover labels -4 as an integer but says it cannot also be rational. Which statement correctly checks this claim?
The claim is correct because negative integers cannot be rational.The claim is incorrect because -4 can be written as -4/1, so it is both an integer and a rational number.The claim is correct because a number can belong to only one number set.The claim is incorrect because -4 is a natural number.
Correct. Since -4 = -4/1, it is rational as well as an integer.
Try writing -4 as a fraction and remember that number sets can be nested.
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Keşif Araçlarının Verilerindeki Karışıklık
TR
ARC_G09_NUM_02_STORY_03
Keşif Araçlarının Verilerindeki Karışıklık
The Rover Data Mix-Up
EN
ARC_G09_NUM_02_STORY_03
The Rover Data Mix-Up