What is the best approximation of the root of 51?
A. 5.9
B. 5.3
C. 9.2
D. 7.1
The Correct Answer and Explanation is :
The correct answer is: D. 7.1
To approximate the square root of 51, we can analyze the options provided:
A. 5.9
B. 5.3
C. 9.2
D. 7.1
Step 1: Identify Perfect Squares
First, we find perfect squares near 51 to guide our estimation. The perfect squares closest to 51 are:
- (7^2 = 49)
- (8^2 = 64)
Since (51) lies between (49) and (64), we know that the square root of (51) will be between (7) and (8).
Step 2: Narrow Down the Options
From our options, only (5.9), (5.3), (9.2), and (7.1) fall within this range.
- 5.3 and 5.9 are both less than 7, so they can be ruled out because we already established that (\sqrt{51}) must be greater than (7).
- 9.2 is too high since (\sqrt{51}) should be less than (8).
Step 3: Compare the Remaining Option
That leaves us with (7.1). To verify if (7.1) is a good approximation for (\sqrt{51}), we can square (7.1):
[
7.1^2 = 50.41
]
This is quite close to (51). To further assess accuracy, we can check (7.2) as well:
[
7.2^2 = 51.84
]
This indicates that (\sqrt{51}) is indeed between (7.1) and (7.2). Since (7.1) yields (50.41), it is the best approximation provided in the options.
Conclusion
Thus, the best approximation of (\sqrt{51}) from the options given is D. 7.1. This option falls within the expected range and is closest to the actual value of (\sqrt{51}), which is approximately (7.14).