Question

which number is closest to $-sqrt{190}$? -13.7 -14.3 -13.3 -12.8

Explanation:

Step1: Find $\sqrt{190}$ approximate value

First, note that $13^2=169$, $14^2=196$. Calculate $13.7^2 = 13.7\times13.7 = 187.69$, $13.8^2=13.8\times13.8=190.44$. So $\sqrt{190}\approx13.78$.

Step2: Find $-\sqrt{190}$ value

$-\sqrt{190}\approx-13.78$

Step3: Compare with options

Calculate differences:
$|-13.78 - (-13.7)| = 0.08$
$|-13.78 - (-14.3)| = 0.52$
$|-13.78 - (-13.3)| = 0.48$
$|-13.78 - (-12.8)| = 0.98$
The smallest difference is 0.08, corresponding to -13.7.

Answer:

-13.7