Which integer is closest to √55 ?
The Correct Answer and Explanation is:
The integer closest to √55 is 7.
Explanation:
To determine the integer closest to √55, we first need to estimate the value of √55 and find out which whole number it is nearest to.
- Identify perfect squares around 55:
- The perfect square less than 55 is 49, and its square root is 7 (since 7 × 7 = 49).
- The perfect square greater than 55 is 64, and its square root is 8 (since 8 × 8 = 64).
Therefore, we know that √55 lies between 7 and 8, as 49 < 55 < 64.
- Narrow down the value:
- Next, we can estimate the square root of 55. Using a calculator, √55 ≈ 7.416.
- Compare to the nearest integers:
- The value of √55 is approximately 7.416, which is closer to 7 than 8. To confirm, let’s calculate the squares of the integers 7 and 8:
- 7 × 7 = 49
- 8 × 8 = 64
- The difference between 55 and 49 (7²) is 55 – 49 = 6.
- The difference between 64 (8²) and 55 is 64 – 55 = 9.
Since 6 is smaller than 9, the square root of 55 is closer to 7 than to 8.
- Conclusion:
- Based on this, the integer closest to √55 is 7, because √55 is approximately 7.416, and it is nearer to 7 than to 8.
By understanding the placement of √55 between perfect squares and comparing the distances to the nearest integers, we confirm that 7 is the closest integer.