Question

which number is closest to \\(\sqrt{126}\\) ? 11.2 10.8 11.6 12.4

Explanation:

Step1: Find nearby perfect squares

We know $11^2=121$ and $12^2=144$, so $\sqrt{126}$ is between 11 and 12.

Step2: Calculate square of each option

• $11.2^2 = 11.2\times11.2 = 125.44$
• $10.8^2 = 10.8\times10.8 = 116.64$
• $11.6^2 = 11.6\times11.6 = 134.56$
• $12.4^2 = 12.4\times12.4 = 153.76$

Step3: Find difference from 126

• $|126 - 125.44| = 0.56$
• $|126 - 116.64| = 9.36$
• $|126 - 134.56| = 8.56$
• $|126 - 153.76| = 27.76$

Step4: Identify smallest difference

The smallest difference is 0.56, corresponding to 11.2.

Answer:

11.2