During a software upgrade aboard an interstellar spacecraft, Nova and Luna monitored the navigation system as it generated several possible calibration formulas. Each formula contained square root expressions that represented different adjustments to the flight controls. To find the correct configuration, they simplified the radical expressions, compared the resulting values, and checked each option against the system requirements. Some configurations produced similar results, but only one matched all the necessary conditions for accurate navigation. After selecting the verified formula, Nova and Luna completed the upgrade, and the spacecraft continued its voyage with a precise and reliable guidance system.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Rewrite 75 using a perfect square factor.
Nova and Luna compare two calibration formulas: Formula A = sqrt(75) and Formula B = 5sqrt(3). Which conclusion is correct?
Formula A is greater than Formula BFormula A and Formula B are equivalentFormula A is smaller than Formula BFormula A cannot be simplifiedCorrect! sqrt(75) = sqrt(25*3) = 5sqrt(3), so the two formulas match.
Try simplifying the radical expression before comparing the formulas.
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Hint
Find each square root first, then subtract the second value from the first.
The navigation system checks the expression sqrt(100) - sqrt(36). What integer value does the system calculate?
Correct! sqrt(100) = 10 and sqrt(36) = 6, so the difference is 4.
Check the square root values and the subtraction step.
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Hint
Look for the largest perfect square factor of 32.
The spacecraft software tests two possible calibration values: sqrt(32) and 3sqrt(2). Which statement correctly compares them?
sqrt(32) is equal to 3sqrt(2)sqrt(32) is smaller than 3sqrt(2)sqrt(32) is equal to 4sqrt(2)sqrt(32) cannot be simplifiedCorrect! sqrt(32) = sqrt(16*2) = 4sqrt(2).
Check the simplification by factoring out a perfect square.
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