OG Square root of Sci Notation Q

AbeNeedsAnswers wrote:(4.8 x 10^9)^(1/2) is closest in value to

(A) 2,200
(B) 70,000
(C) 220,000
(D) 7,000,000
(E) 22,000,000

B

Two IMPORTANT concepts:
1) n^(1/2) = √n
2) √(xy) = (√x)(√y)

So, (4.8 x 10^9)^(1/2) = √(4.8 x 10^9) by Rule #1
= √(48 x 10^8)
= (√48) (√10^8) by Rule #2
≈ (7)(10^4)
≈ (7)(10,000)
≈ 70,000

Answer: B

Hi AbeNeedsAnswers,

This question can actually be solved by breaking the prompt down into 'pieces' (and using a bit of estimation on one of them).
Let's start with two things you probably already know: 10^2 = 100 and √100 = 10

Using Exponent Rules, we can break down (4.8 x 10^9) into 5 'pieces':
(4.8 x 10)(10^2)(10^2)(10^2)(10^2)

Next we have to square-root all of this. Since this is just a big product, using Radical Rules, we are allowed to square-root each piece... When we do, we get...

(about 7)(10)(10)(10)(10) =
(about 7)(10,000) =
about 70,000

Final Answer: B

GMAT assassins aren't born, they're made,
Rich