Question

use the calculator below to approximate \\(\sqrt{45}\\) 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.

Explanation:

Step1: Identify nearby perfect squares

We know $6^2=36$ and $7^2=49$, so $\sqrt{45}$ is between 6 and 7.

Step2: Narrow down to tenths range

Calculate $6.7^2 = 6.7\times6.7 = 44.89$
Calculate $6.8^2 = 6.8\times6.8 = 46.24$

Step3: Compare to target value

$44.89 < 45 < 46.24$, and 45 is closer to 44.89.

Answer:

6.7