While exploring a newly discovered asteroid, Emek and Tara collected mineral samples and recorded measurements such as -7, 5/8, 3.125, √49, and √11. Before storing the data, the research archive required every value to be classified within the real number system. They identified which measurements were integers, rational numbers, and irrational numbers, noting that some values belonged to more than one set. After organizing the data, they compared the most important readings to identify the richest mineral deposits. Their accurate classifications and comparisons completed the scientific survey and helped the research team select the best samples for further study.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Simplify any square roots before classifying the numbers.
Which measurement belongs to both the set of integers and the set of rational numbers?
√115/8√493.125Correct! √49 = 7, which is an integer and therefore also a rational number.
Simplify the square root first, then decide which number sets it belongs to.
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Hint
Evaluate √49 before counting the integers.
Among the measurements -7, 5/8, 3.125, √49, and √11, how many are integers?
Correct! There are 2 integers.
Remember that √49 is equal to 7, which is an integer.
Next🎉 Congrats! You got this question!
Hint
Use decimal values: 5/8 = 0.625, √11 ≈ 3.32, and √49 = 7.
Which list shows the measurements in order from least to greatest?
-7, 5/8, 3.125, √11, √49-7, 3.125, 5/8, √11, √495/8, -7, 3.125, √49, √11-7, 5/8, √49, 3.125, √11Correct! The numbers increase as -7, 0.625, 3.125, about 3.32, and 7.
Compare the decimal values of the fraction and square roots before ordering the numbers.
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🎉 Congrats! You finished this challenge set!




