Question

use the calculator below to approximate \\(\sqrt{134}\\) as a decimal to the tenths place. note that you must do the approximation without using a square root button. your answer must be within a tenth of the actual value. \\(\sqrt{134}\\ \approx\\ \square\\)

Explanation:

Step1: Find integer bounds for $\sqrt{134}$

We know $11^2=121$ and $12^2=144$, so $11 < \sqrt{134} < 12$.

Step2: Test midpoint 11.6

Calculate $11.6^2 = 11.6 \times 11.6 = 134.56$

Step3: Test lower value 11.5

Calculate $11.5^2 = 11.5 \times 11.5 = 132.25$

Step4: Compare to 134

$132.25 < 134 < 134.56$, so $\sqrt{134}$ is between 11.5 and 11.6. Since 134 is closer to 134.56, we round to the tenths place.

Answer:

11.6