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Question
Compare Start Root 27 End Root and Start Fraction 22 over 3 End Fraction using either <, >, or =.
(1 point)
Responses
Start Root 27 End Root < Start Fraction 22 over 3 End Fraction
Image with alt text: Start Root 27 End Root < Image with alt text: Start Fraction 22 over 3 End Fraction
Start Root 27 End Root > Start Fraction 22 over 3 End Fraction
Image with alt text: Start Root 27 End Root > Image with alt text: Start Fraction 22 over 3 End Fraction
Start Root 27 End Root = Start Fraction 22 over 3 End Fraction
Image with alt text: Start Root 27 End Root = Image with alt text: Start Fraction 22 over 3 End Fraction
Start Root 27 End Root < Start Fraction 22 over 3 End Fraction
To compare √27 and 22/3, we need to simplify both expressions:
√27 = 3√3
22/3 = 7 1/3
Now, we can see that 3√3 is less than 7 1/3. Therefore, the correct comparison is:
√27 < 22/3
To compare the expressions Start Root 27 End Root and Start Fraction 22 over 3 End Fraction, we can simplify both expressions to a common form.
Start Root 27 End Root can be simplified as Start Root 3 ^ 3 End Root, since 27 is equal to 3 raised to the power of 3.
Start Fraction 22 over 3 End Fraction is already simplified.
Now, we compare the simplified expressions:
Start Root 3 ^ 3 End Root vs. Start Fraction 22 over 3 End Fraction
Cubing 3 gives us 27, so Start Root 3 ^ 3 End Root is equal to Start Root 27 End Root.
Therefore, Start Root 27 End Root is equal to Start Fraction 22 over 3 End Fraction.
Hence, the correct symbol to compare them is Start Root 27 End Root = Start Fraction 22 over 3 End Fraction.