Which of the following is the closest approximation to $$\frac{\left[[\sqrt{73}\cdot\sqrt{239}\ \right]}{\left[\sqrt{7.2}+\sqrt{15.7}\right]}$$
A. 10
B. 15
C. 20
D. 25
E. 30
What's the best way to determine the correct answer here?

Hi Roland2rule,
Let's take a look at your question.

$$\frac{\sqrt{73}\sqrt{239}}{\sqrt{7.2}+\sqrt{15.7}}$$
We are asked to approximate its value, so let's first approximate all the numbers used in the square roots with the closest possible number that is a perfect square.
Using approximation we can rewrite the given expression as,
$$\approx\frac{\sqrt{81}\sqrt{225}}{\sqrt{9}+\sqrt{16}}$$

Now it seems pretty simple to evaluate it, since all the numbers are now perfect squares.
$$\approx\frac{9\times15}{3+4}$$
$$\approx\frac{9\times15}{7}$$

To make the calculation more simple, let's write 14 instead of 15 in the numerator because it is the multiple of 7 closest to 15.
So the expression will look like:
$$\approx\frac{9\times14}{7}$$
$$\approx9\times2\approx18$$

The closest possible value to 18 in the given options is 20.
Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.