Arithmetic- roots

[BTGmoderatorRO]

$$\sqrt{\left[\left(4.9\right)\cdot\left(10^9\right)\right]}\ is\ closest\ to\ which\ of\ the\ following?$$
A. 7,000
B. 70,000
C. 14,000
D. 22,000
E. 220,000
what is the correct approach to use here? My headache is getting higher with this question
Thanks?

[EconomistGMATTutor]

$$\sqrt{\left[\left(4.9\right)\cdot\left(10^9\right)\right]}\ is\ closest\ to\ which\ of\ the\ following?$$
A. 7,000
B. 70,000
C. 14,000
D. 22,000
E. 220,000

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

$$\sqrt{\left(4.9\right)\times10^9}$$
Let's write 10^9 as 10 * 10^8, we actually want to eliminate the decimal point from 4.9
$$=\sqrt{4.9\times10\times10^8}$$
$$=\sqrt{49\times10^8}$$
$$=\sqrt{49}\times\sqrt{10^8}$$
$$=7\times\sqrt{10^8}$$
$$=7\times\sqrt{\left(10^4\right)^2}$$
$$=7\times10^4$$
$$=70,000$$

Therefore, Option B is correct.

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