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by Brent@GMATPrepNow » Tue Jul 25, 2017 7:49 pm
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
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by [email protected] » Thu Jul 27, 2017 12:24 pm
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

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by Matt@VeritasPrep » Mon Aug 07, 2017 12:09 am
The answers differ by powers of 10, so we can afford some clumsy approximation:

√4.8 * √10� ≈

2 * √10� * √10 ≈

2 * 10� * 3 ≈

6 * 10000

Only B is at all close.
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by Jeff@TargetTestPrep » Wed Aug 09, 2017 12:42 pm
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
√(4.8 x 10^9) is equivalent to √(48 x 10^8), which equals:

√48 x √10^8 = 4√3 x 10^4 = 4 x 1.7 x 10,000 = 68,000 or about 70,000.

Alternative solution:

√(4.8 x 10^9) is equivalent to √(48 x 10^8), which is about √(49 x 10^8). We choose the number 49 because 49 is a perfect square. Now let's simplify √(49 x 10^8):

√49 x √10^8 = 7 x 10^4 = 70,000

Answer: B

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