Final answer:
To approximate √8 to one decimal place without a calculator, we note that 2^2=4 and 3^2=9, so √8 is between 2 and 3. Since 8 is closer to 9, √8 is slightly less than 3, making 2.8 the closest one decimal place approximation. None of the provided options are correct.
Step-by-step explanation:
The question asks to approximate the irrational number √8 to one decimal place without using a calculator.
First, we need to find two perfect squares between which √8 lies. We know that 2^2=4 and 3^2=9.
Since 8 is between 4 and 9, √8 must be between 2 and 3.
Using estimation, we can approximate that √8 is closer to √9 than √4 because 8 is closer to 9 than to 4.
Since √9=3, we can say that √8 is slightly less than 3.
Throughout this estimation process, we can conclude that the closest one decimal place approximation would be 2.8. Therefore, none of the given options are the correct approximation.