A pendulum is $L$ meters long. The time, $t$, in seconds that it takes to swing back and forth once is given by $t=2 \sqrt{L}$. Suppose the pendulum takes 5.72 seconds to swing back and forth once. What is its length?
Carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.
7 meters
$\times \quad 5$

Step 1 ：The problem provides the time it takes for the pendulum to swing back and forth once, which is 5.72 seconds. It also provides the formula for the time, $t=2 \sqrt{L}$, where $L$ is the length of the pendulum.

Step 2 ：We need to find the length of the pendulum, so we rearrange the formula to solve for $L$. We square both sides to get rid of the square root, giving us $t^2 = 4L$.

Step 3 ：Then, we divide both sides by 4 to isolate $L$, giving us the formula $L = \frac{t^2}{4}$.

Step 4 ：We substitute the given time of 5.72 seconds into this formula to find the length of the pendulum. So, $L = \frac{(5.72)^2}{4}$.

Step 5 ：Calculating the above expression, we find that $L = 8.179599999999999$.

Step 6 ：Rounding to the nearest tenth, we find that the length of the pendulum is approximately \(\boxed{8.2}\) meters.