Question

which number is closest to $-sqrt{128}$? -12.2 -10.7 -10.6 -11.3 submit

Explanation:

Step1: Calculate the value of $-\sqrt{128}$

First, we know that $\sqrt{121} = 11$ and $\sqrt{144}=12$, and $128$ is between $121$ and $144$. Also, we can simplify $\sqrt{128}=\sqrt{64\times2} = 8\sqrt{2}\approx8\times1.414 = 11.312$. So $-\sqrt{128}\approx - 11.312$.

Step2: Calculate the absolute differences

• For $-12.2$: The absolute difference is $|-12.2 - (-11.312)|=| - 0.888| = 0.888$.
• For $-10.7$: The absolute difference is $|-10.7 - (-11.312)|=|0.612| = 0.612$.
• For $-10.6$: The absolute difference is $|-10.6 - (-11.312)|=|0.712| = 0.712$.
• For $-11.3$: The absolute difference is $|-11.3 - (-11.312)|=|0.012| = 0.012$.

Step3: Compare the absolute differences

We compare the absolute differences: $0.012<0.612<0.712<0.888$. The smallest absolute difference is with $-11.3$.

Answer:

-11.3