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OG Square root of Sci Notation Q

This topic has 4 expert replies and 0 member replies
AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG Square root of Sci Notation Q

Post 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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    Post 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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    Post 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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    GMAT/MBA Expert

    Post 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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    Post 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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