Question

When square root of 189 is written as a simplified mixed radical the coefficient is Answer __ and the radicand is Answer __.

Answer 1

The velocity of a falling object can be found using the formula v space equals space square root of 64 h end root, where v is the velocity of the object in feet per second, and h is the distance the object has already fallen in feet. Determine the exact velocity of an object after it has fallen 7 feet in simplified form.

Answer 2

The square root of 189 can be simplified as $\sqrt{189} = \sqrt{9 \cdot 21} = \sqrt{9} \cdot \sqrt{21} = 3 \cdot \sqrt{21}$.

Therefore, the coefficient is $\boxed{3}$ and the radicand is $\boxed{21}$.

Answer 3

To find the exact velocity of an object after it has fallen 7 feet using the formula $v = \sqrt{64h}$, we substitute $h = 7$ into the formula:

$v = \sqrt{64 \cdot 7} = \sqrt{448} = \sqrt{64 \cdot 7} = \sqrt{64} \cdot \sqrt{7} = 8 \cdot \sqrt{7} = \boxed{8\sqrt{7}}$ feet per second.