I am trying to complete the question below, but I am not sure how to simplify the radical. What I have so far is
$$(5.8\sqrt{40} + 56.4) – (5.8\sqrt{10} + 56.4) \;=\; \text{the difference}$$
How does one simplify this expression without a calculator?
The formula $E = 5.8\sqrt{x} + 56.4$ models the projected number of elderly Americans ages $65$–$84$, $E$, in millions, $x$ years after $2020$.
a. Use the formula to find the projected increase in number of Americans ages $65.84$, in millions from $2030$ to $2060$. Express this difference in simplified radical form.
b. Use a calculator and write your answer in part (a) to the nearest tenth.
Best Answer
Answer from the comments.
Since $\sqrt{40} = \sqrt{4} \sqrt{10} = 2 \sqrt{10}$, the difference is:
$$5.8 \cdot 2 \sqrt{10} - 5.8 \sqrt{10} = 5.8\sqrt{10} (2-1) = 5.8\sqrt{10}$$
which is $18.3$ million, rounding down to the nearest tenth (of a million).
This answer is the right order of magnitude as there are around $330$ million Americans, so the change in this age group should be an order of magnitude less.