Question

which number is closest to $-sqrt{218}$? -14.1 -15.5 -14.3 -14.7 submit

Explanation:

Step1: Calculate the square of each option's absolute value

First, find the absolute value of each option and square it.

• For -14.1: $| - 14.1|=14.1$, $(14.1)^2 = 14.1\times14.1 = 198.81$
• For -15.5: $| - 15.5| = 15.5$, $(15.5)^2=15.5\times15.5 = 240.25$
• For -14.3: $| - 14.3| = 14.3$, $(14.3)^2=14.3\times14.3 = 204.49$
• For -14.7: $| - 14.7| = 14.7$, $(14.7)^2=14.7\times14.7 = 216.09$

Step2: Compare with 218

We know that $(\sqrt{218})^2 = 218$. Now we find the difference between each squared value and 218:

• For 198.81: $|218 - 198.81| = 19.19$
• For 240.25: $|240.25 - 218| = 22.25$
• For 204.49: $|218 - 204.49| = 13.51$
• For 216.09: $|218 - 216.09| = 1.91$

The smallest difference is 1.91, which corresponds to the number -14.7.

Answer:

-14.7