Inside an advanced spacecraft, Nova and Luna inspected the reactor before a long exploration mission. The energy calibration software displayed several power settings using expressions with square roots, but the reactor could not start until the values were verified. They simplified the radical expressions, checked equivalent forms, and compared the results with the required energy levels. After confirming the correct calculations, they entered the updated settings into the reactor system. The crystal-powered engine reached a stable output, and the spacecraft was ready to begin its mission safely.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Look for a perfect square factor inside the radical.
The reactor software displayed the energy expression sqrt(50). Which simplified form is equivalent to this expression?
5sqrt(2)10sqrt(5)25sqrt(2)sqrt(25)Correct! sqrt(50) can be written as sqrt(25*2), which simplifies to 5sqrt(2).
Check whether the number inside the square root contains a perfect square factor.
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Hint
Find the square root of each perfect square separately, then add the results.
The reactor system uses the expression sqrt(81) + sqrt(16) for a calibration check. What is the value of this expression?
Correct! sqrt(81) = 9 and sqrt(16) = 4, so the total is 13.
Review the values of the square roots before adding them.
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Hint
Rewrite 72 as a product containing a perfect square.
Nova and Luna compare two reactor settings: sqrt(72) and 6sqrt(2). Which statement is correct?
sqrt(72) is smaller than 6sqrt(2)sqrt(72) and 6sqrt(2) are equivalentsqrt(72) is equal to 3sqrt(2)sqrt(72) cannot be simplifiedCorrect! sqrt(72) = sqrt(36*2) = 6sqrt(2), so the settings are equivalent.
Try simplifying the radical before comparing the expressions.
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