26. What is the best decimal approximation of 10 × the positive square root of 207?
Answer: D
89.4
To find the best decimal approximation of 10 times the positive square root of 207, we calculate \(10 \times \sqrt{207}\). This results in approximately 89.4, making it the most accurate choice among the options provided.
A) 100
Option A is incorrect because 100 is significantly higher than the calculated value of 89.4. The square root of 207 is approximately 14.4, and when multiplied by 10, the result is notably less than 100.
B) 44.7
Option B is also incorrect as it underestimates the value of 10 times the square root of 207. The correct calculation yields a value higher than 44.7, indicating that this option does not reflect the accurate approximation.
C) 200
Option C is incorrect because 200 far exceeds the correct value of 89.4. The calculation of 10 times the positive square root of 207 does not approach this high figure, thus making it an inaccurate approximation.
D) 89.4
Option D is correct as it closely approximates the value of 10 times the positive square root of 207. This is the best choice based on the mathematical calculation, confirming its accuracy.
Conclusion
The correct answer is 89.4 because it accurately represents 10 times the positive square root of 207. All other options either underestimate or overestimate this value, confirming that D is the only valid choice based on the calculations involved.