0
$\begingroup$

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.

$\endgroup$
6
  • 4
    $\begingroup$ $\sqrt{40}=\sqrt4\sqrt{10}=2\sqrt{10}$ $\endgroup$
    – J. W. Tanner
    Commented Feb 8, 2021 at 0:33
  • 2
    $\begingroup$ $(2x\sqrt{10} + y) - (x\sqrt{10} + y) = x\sqrt{10}.$ $\endgroup$
    – user2661923
    Commented Feb 8, 2021 at 0:34
  • $\begingroup$ so $(11.6\sqrt{10} + 56.4) - (5.8\sqrt{10} + 56.4)$ is the simplified radical form? $\endgroup$
    – Grant
    Commented Feb 8, 2021 at 0:40
  • 2
    $\begingroup$ Note: $56.4-56.4=0$ $\endgroup$
    – J. W. Tanner
    Commented Feb 8, 2021 at 0:44
  • 3
    $\begingroup$ I get it now, so $5.8\sqrt{10}$ is the simplified radical form. $\endgroup$
    – Grant
    Commented Feb 8, 2021 at 0:48

1 Answer 1

Reset to default
0
$\begingroup$

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.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .