Determine which two values the following expression is between.
√37
A. 7 and 8
B. 5 and 6
C. 4 and 5
The Correct Answer and Explanation is:
To determine which two values the square root of (37) ((\sqrt{37})) lies between, let’s first identify the perfect squares closest to (37):
- (6^2 = 36)
- (7^2 = 49)
Thus, (36 < 37 < 49). This means (\sqrt{37}) is greater than (6) but less than (7), so the correct answer is:
A. 7 and 8
Explanation:
The square root function identifies a number that, when squared, equals the given value. For example, (\sqrt{36} = 6) because (6^2 = 36), and (\sqrt{49} = 7) because (7^2 = 49). For non-perfect squares, such as (37), the square root will be a decimal between the square roots of the two nearest perfect squares.
Here’s why (\sqrt{37}) lies between (6) and (7):
- (6^2 = 36), which is less than (37), so (\sqrt{37} > 6).
- (7^2 = 49), which is greater than (37), so (\sqrt{37} < 7).
Since (37) is just slightly larger than (36), (\sqrt{37}) will be slightly greater than (6). Performing a rough estimation:
[
\sqrt{37} \approx 6.08
]
This confirms that it falls between (6) and (7).
If you were to test the other options:
- Option B: (5) and (6): (\sqrt{37}) cannot fit here because (37 > 36) ((6^2)), and (\sqrt{37} > 6).
- Option C: (4) and (5): This is even less plausible, as (37) is much larger than (25) ((5^2)).
Thus, the answer is A. 6 and 7.