Question

(a) Melissa accidentally drops a pair of sunglasses from the top of a roller coaster, 64 feet above the ground. Simplify $\sqrt{\frac{64}{16}}$to determine the number of seconds it takes for the sunglasses to reach the ground.

(b) Suppose the sunglasses in the previous example were dropped from a height of 144 feet. Simplify $\sqrt{\frac{144}{16}}$to determine the number of seconds it takes for the sunglasses to reach the ground.

Short answer

Part (a) 2 seconds

Part (b) 3 seconds

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

Melissa accidentally drops a pair of sunglasses from the top of a roller coaster, 64 feet above the ground.

We have to simplify $\sqrt{\frac{64}{16}}$to determine the number of seconds it takes for the sunglasses to reach the ground.

Part (a) Step 2. Simplify the given expression.

$\sqrt{\frac{64}{16}}$

Simplify the fraction inside the radical first. Rewrite showing common factors,

$\sqrt{\frac{16·4}{16}}$

Simplify the fraction by removing common factors,

$\sqrt{4}=2$

It will take 2 seconds for the sunglasses to reach the ground.

Part (b) Step 1. Given information.

Suppose the sunglasses in the previous example were dropped from a height of 144 feet.

We have to simplify$\sqrt{\frac{144}{16}}$to determine the number of seconds it takes for the sunglasses to reach the ground.

Part (b) Step 2. Simplify the given expression.

$\sqrt{\frac{144}{16}}$

Simplify the fraction inside the radical first. Rewrite showing common factors,

$\sqrt{\frac{16·9}{16}}$

Simplify the fraction by removing common factors,

$\sqrt{9}=3$

It will take 3 seconds for the sunglasses to reach the ground.