What is the best decimal approximation of 10 × the positive square root of 20?

Rationale

44.7 is the best decimal approximation of 10 times the positive square root of 20.

The square root of 20 is approximately 4.47. When this number is multiplied by 10, the result is approximately 44.7. Therefore, choice C) is the correct answer.

A (89.4) YOUR ANSWER

This choice might be selected if one mistakenly thought that the square root of 20 is 8.94. However, the square root of 20 is approximately 4.47, not 8.94. Therefore, 10 times the square root of 20 could not be 89.4.

B (200) YOUR ANSWER

This choice might be selected if one mistakenly thought that 10 times 20 is the correct operation. However, the task is to multiply 10 by the square root of 20, not 20 itself. Therefore, 200 is not the correct answer.

D (100) YOUR ANSWER

This choice might be selected if one mistakenly thought that the square root of 20 is 10. However, the square root of 20 is approximately 4.47, not 10. Therefore, 10 times the square root of 20 could not be 100.

Conclusion

The correct operation for this problem is to multiply 10 by the square root of 20, which is approximately 4.47. When 10 is multiplied by 4.47, the result is approximately 44.7. This is why choice C) is the correct answer. The other choices may be selected if one makes a mistake in either the square root calculation or the multiplication.

What is the best decimal approximation of 10 × the positive square root of 20?

44.7 is the best decimal approximation of 10 times the positive square root of 20.

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