Question

which number is closest to $-sqrt{114}$? -9.5 -10.6 -11.1 -10.1 submit

Explanation:

Step1: Calculate the value of $\sqrt{114}$

We know that $10^2 = 100$ and $11^2 = 121$. So $\sqrt{114}$ is between 10 and 11. Let's calculate it more precisely. $10.6^2 = 112.36$, $10.7^2 = 114.49$. So $\sqrt{114}\approx10.68$. Then $-\sqrt{114}\approx - 10.68$.

Step2: Find the difference between -10.68 and each option

• For -9.5: $|-10.68 - (-9.5)| = |-1.18| = 1.18$
• For -10.6: $|-10.68 - (-10.6)| = |-0.08| = 0.08$
• For -11.1: $|-10.68 - (-11.1)| = |0.42| = 0.42$
• For -10.1: $|-10.68 - (-10.1)| = |-0.58| = 0.58$

Step3: Compare the differences

The smallest difference is 0.08, which corresponds to the number -10.6.

Answer:

-10.6