During an asteroid exploration mission, Nova and Luna received measurement reports from a mining drone searching for valuable minerals. The drone recorded the estimated deposits using expressions with square roots, but the crew needed simplified values before comparing the locations. Nova and Luna reduced the radical expressions, converted equivalent forms when needed, and analyzed the results from each area of the asteroid. Their calculations revealed which deposit had the greatest potential value. With the correct excavation site selected, the mining crew began operations efficiently and prepared the collected resources for the next stage of the mission.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Find the largest perfect square factor of 98.
The mining drone recorded a mineral estimate as sqrt(98). Which simplified expression represents this value?
7sqrt(2)14sqrt(7)49sqrt(2)7sqrt(14)Correct! sqrt(98) = sqrt(49*2) = 7sqrt(2).
Try rewriting the number inside the radical using a perfect square factor.
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Hint
Evaluate each square root before adding.
The drone compared two mineral measurements: sqrt(64) + sqrt(25). What is the total value of these two measurements?
Correct! sqrt(64) = 8 and sqrt(25) = 5, giving a total of 13.
Check the values of the perfect square roots and add them carefully.
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Hint
Rewrite 45 as a product containing a perfect square.
Nova and Luna compare two asteroid deposits with estimates sqrt(45) and 3sqrt(5). Which statement is true?
sqrt(45) is greater than 3sqrt(5)sqrt(45) is smaller than 3sqrt(5)sqrt(45) and 3sqrt(5) represent the same valuesqrt(45) cannot be simplifiedCorrect! sqrt(45) = sqrt(9*5) = 3sqrt(5), so the estimates are equal.
Simplify the radical expression before comparing the two values.
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