\(\sqrt{{4.8}\times{10^9}}\) is closest in value to

(A) 2,200

(B) 70,000

(C) 220,000

(D) 7,000,000

(E) 22,000,000

As in all direct calculation problems, you should pause for about 20 seconds and consider your options. You should also scan your answers, but this is standard operating procedure for all PS (problem solving) questions.

Here the answers reflect different powers of 10, and we can use that to eliminate some of our answers. In general, taking the square root of a number cuts the number of digits in half. For example, \(\sqrt{6400} = 80\). However, there are exceptions like \(\sqrt{900} = 30\).

\({4.8}\times{10^9}\) has 10 digits, so the square root will have 5 or 6 digits. Consequently, we can eliminate A, D, and E. At this point it make more sense to work backwards than to directly calculate or approximateÂ \(\sqrt{{4.8}\times{10^9}}\).

Of the remaining possible answers, B is easier to work with:

\(70,000^2 = {7^2}\times{{10,000}^2} = {49}\times{(10^4)^2}\)

\({49}\times{10^8} = 4,900,000,000\)

That’s are really good approximation.

**The correct answer is B.**

The Official Guide answer is also compelling, and you should definitely take a look.