Question

which number is closest to $-sqrt{71}$? -7.9 -9.1 -8.4 -8.8

Explanation:

Step1: Find the value of $\sqrt{71}$

We know that $8^2 = 64$ and $9^2 = 81$. So $\sqrt{71}$ is between 8 and 9. Let's calculate a more precise value. $8.4^2 = 70.56$ and $8.5^2 = 72.25$. Since $71$ is closer to $70.56$ than to $72.25$, $\sqrt{71}\approx 8.436$. Then $-\sqrt{71}\approx -8.436$.

Step2: Calculate the absolute differences

• For -7.9: $|-8.436 - (-7.9)| = |-0.536| = 0.536$
• For -9.1: $|-8.436 - (-9.1)| = |0.664| = 0.664$
• For -8.4: $|-8.436 - (-8.4)| = |-0.036| = 0.036$
• For -8.8: $|-8.436 - (-8.8)| = |0.364| = 0.364$

Step3: Compare the differences

The smallest difference is 0.036, which corresponds to -8.4.

Answer:

-8.4