Answer :
To estimate the square root of 1,398, we can follow these steps:
1. Identify Nearby Perfect Squares: First, we look for perfect squares that are close to 1,398. We know:
- [tex]\( 37^2 = 1,369 \)[/tex]
- [tex]\( 38^2 = 1,444 \)[/tex]
From this, we observe that [tex]\(\sqrt{1,398}\)[/tex] is between 37 and 38 because 1,398 is between 1,369 and 1,444.
2. Narrow Down the Approximation: Considering the options provided:
- 38.1
- 37.2
- 37.4
- 36.9
We can narrow our choice based on how close 1,398 is to the nearby perfect squares:
- 1,398 is closer to 1,369 than it is to 1,444. Therefore, [tex]\(\sqrt{1,398}\)[/tex] should be closer to 37 than to 38.
3. Select the Correct Option: Given the result from the accurate computation, the closest approximate value is [tex]\(37.4\)[/tex].
Thus, the estimated value of [tex]\(\sqrt{1,398}\)[/tex] is closest to 37.4.
1. Identify Nearby Perfect Squares: First, we look for perfect squares that are close to 1,398. We know:
- [tex]\( 37^2 = 1,369 \)[/tex]
- [tex]\( 38^2 = 1,444 \)[/tex]
From this, we observe that [tex]\(\sqrt{1,398}\)[/tex] is between 37 and 38 because 1,398 is between 1,369 and 1,444.
2. Narrow Down the Approximation: Considering the options provided:
- 38.1
- 37.2
- 37.4
- 36.9
We can narrow our choice based on how close 1,398 is to the nearby perfect squares:
- 1,398 is closer to 1,369 than it is to 1,444. Therefore, [tex]\(\sqrt{1,398}\)[/tex] should be closer to 37 than to 38.
3. Select the Correct Option: Given the result from the accurate computation, the closest approximate value is [tex]\(37.4\)[/tex].
Thus, the estimated value of [tex]\(\sqrt{1,398}\)[/tex] is closest to 37.4.