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## OG Square root of Sci Notation Q

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 0 member replies
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#### OG Square root of Sci Notation Q

Tue Jul 25, 2017 7:39 pm
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
(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

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Brent@GMATPrepNow GMAT Instructor
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Tue Jul 25, 2017 7:49 pm
(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

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Thu Jul 27, 2017 12:24 pm

This question can actually be solved by breaking the prompt down into 'pieces' (and using a bit of estimation on one of them).

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...

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

√4.8 * √10⁹ ≈

2 * √10⁸ * √10 ≈

2 * 10⁴ * 3 ≈

6 * 10000

Only B is at all close.

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Wed Aug 09, 2017 12:42 pm
(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

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