Question

which number is closest to $-sqrt{355}$? -18.8 -19.3 -18.1 -17.5

Explanation:

Step1: Calculate the square root of 355

First, we know that \( 18^2 = 324 \) and \( 19^2 = 361 \). So \( \sqrt{355} \) is between 18 and 19. Let's calculate \( 18.8^2 = 18.8\times18.8 = 353.44 \), \( 19.3^2 = 19.3\times19.3 = 372.49 \), \( 18.1^2 = 18.1\times18.1 = 327.61 \), \( 17.5^2 = 17.5\times17.5 = 306.25 \). And \( 18.8^2 = 353.44 \), \( 18.9^2 = 18.9\times18.9 = 357.21 \). Since \( 353.44 < 355 < 357.21 \), so \( \sqrt{355} \) is between 18.8 and 18.9. And \( 355 - 353.44 = 1.56 \), \( 357.21 - 355 = 2.21 \). Since 1.56 < 2.21, so \( \sqrt{355} \) is closer to 18.8. Then \( -\sqrt{355} \) is closer to -18.8.

Step2: Verify the distance from each option to \(-\sqrt{355}\)

Let \( x = -\sqrt{355} \approx -18.841 \) (more accurately, we can calculate \( \sqrt{355}\approx18.841 \), so \( -\sqrt{355}\approx -18.841 \)). Now calculate the absolute difference between each option and -18.841:

• For -18.8: \( | -18.8 - (-18.841)| = |0.041| = 0.041 \)
• For -19.3: \( | -19.3 - (-18.841)| = | -0.459| = 0.459 \)
• For -18.1: \( | -18.1 - (-18.841)| = |0.741| = 0.741 \)
• For -17.5: \( | -17.5 - (-18.841)| = |1.341| = 1.341 \)

The smallest absolute difference is 0.041, which corresponds to the number -18.8.

Answer:

-18.8