A mysterious deep space transmission reached Emek and Luna with signal strengths written as √12, √20, √30, √50, and √63. To decode the fading message, they estimated each radical using nearby perfect squares and placed the values in order on a number line. While checking the display, they discovered that √30 had been placed to the right of √50, which could not be correct. After moving it to the proper position and verifying every estimate, the signals formed the correct sequence, and the complete message was successfully decoded before it disappeared.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
The square root function increases as the number under the radical increases.
Why was it incorrect to place √30 to the right of √50 on the number line?
Because √30 is greater than √50.Because 30 is less than 50, so √30 is less than √50.Because √30 and √50 are equal.Because √30 is an integer.Correct! Since 30 < 50, it follows that √30 < √50.
Compare the numbers inside the square roots first.
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Hint
Compare 63 with the nearby perfect squares 49 and 64.
What is the exact value of √63 rounded down to the nearest whole number?
Correct! √63 is about 7.94, so rounding down gives 7.
Estimate √63 using the nearest perfect squares.
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Hint
Square root values increase as the numbers under the radicals increase.
Which list shows the correct order of the signal strengths from least to greatest?
√12, √20, √30, √50, √63√20, √12, √30, √50, √63√12, √30, √20, √50, √63√12, √20, √50, √30, √63Correct! Ordering the radicands from least to greatest gives the correct order.
Arrange the numbers under the square roots before comparing their values.
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🎉 Congrats! You finished this challenge set!
