5. If a ball is dropped on the moon from a height of 50 meters, it will take approximately $$ \sqrt{62.5} $$ seconds to hit the ground. Foflow the steps below to find approximately how many seconds it takes the ball to hit the ground. a. Estimate how long it takes the ball to hit the ground by using nearby perfect squares and finding two integers the time is between. It takes between $$ \qquad $$ and $$ \qquad $$ seconds to hit the ground. b. Using a calculator, find the time it takes to hit the ground to the nearest tenth of a second. $$ \qquad $$ 8

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**a. Estimation using perfect squares**

We know that:
$$
7^2 = 49 \quad \text{and} \quad 8^2 = 64
$$
Since:
$$
49 < 62.5 < 64
$$
it follows that:
$$
\sqrt{62.5} \quad \text{is between} \quad 7 \quad \text{and} \quad 8.
$$

**b. Calculating the time using a calculator**

Using a calculator:
$$
\sqrt{62.5} \approx 7.9
$$

Thus, it takes approximately $$7.9$$ seconds for the ball to hit the ground.
It takes between 7 and 8 seconds to hit the ground. Using a calculator, it takes approximately 7.9 seconds.

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