22. What is the best decimal approximation of 10 × the positive square root of 20?
Answer: C
10 × the positive square root of 20 is approximately 44.7.
To find the best decimal approximation of 10 times the positive square root of 20, we calculate \(10 \times \sqrt{20}\). The square root of 20 is approximately 4.472, and when multiplied by 10, it yields approximately 44.7.
A) 89.4
This option is incorrect because multiplying 10 by the square root of 20 results in a value less than 89.4. Specifically, \(10 \times 4.472\) equals approximately 44.7, which is significantly lower than 89.4.
B) 200
This option is also incorrect as it greatly exceeds the calculated value. The product of 10 and the square root of 20 is around 44.7, far less than 200, making this option an inaccurate approximation.
C) 44.7
This option is correct, as it matches the calculated value of \(10 \times \sqrt{20}\) precisely. The square root of 20 is approximately 4.472, and therefore \(10 \times 4.472\) equals about 44.7, confirming this as the best approximation.
D) 100
This option is incorrect because it overestimates the product of 10 times the positive square root of 20. As calculated, \(10 \times \sqrt{20}\) results in approximately 44.7, which is much lower than 100.
Conclusion
The value of 44.7 accurately represents the approximation of 10 times the positive square root of 20, while all other options either significantly overestimate or underestimate this calculation. Therefore, option C is the only viable choice based on the mathematical evaluation provided.