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(4.8*10^9)^1/2 is closest in value to

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(4.8*10^9)^1/2 is closest in value to [#permalink]

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New post 14 Sep 2015, 06:07
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Question Stats:

73% (00:42) correct 27% (00:42) wrong based on 173 sessions

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\(\sqrt{4.8*10^9}\) is closest in value to

(A) 2,200
(B) 70,000
(C) 220,000
(D) 7,000,000
(E) 22,000,000
[Reveal] Spoiler: OA

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Last edited by Bunuel on 14 Sep 2015, 06:22, edited 1 time in total.
Renamed the topic and edited the question.

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Re: (4.8*10^9)^1/2 is closest in value to [#permalink]

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New post 14 Sep 2015, 06:29
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ske wrote:
\(\sqrt{4.8*10^9}\) is closest in value to

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


Solution: \(\sqrt{4.8*10^9}\) = \(\sqrt{48*10^8}\) = \(\sqrt{49*10^8}\) = \(7*10^4\)

Option B

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Re: (4.8*10^9)^1/2 is closest in value to [#permalink]

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New post 20 Sep 2017, 19:03
First method: Estimate

\(\sqrt{4.8 * 10^9}\) < \(\sqrt{10 * 10^9}\)
\(\sqrt{4.8 * 10^9}\) < 100,000

\(\sqrt{4.8 * 10^9}\) is definitely less than 100,000 but close to 100,000 => answer is B




Second method: Calculation

\(\sqrt{4.8 * 10^9}\) =
\(\sqrt{48 * 10^8}\) =

then take square roots of both parts:
\(\sqrt{48}\) * \(\sqrt{10^8}\) =
4\(\sqrt{3}\) * 10^4 =
4 * \(\sqrt{3}\) * 10,000 =
40,000 * 1.7 (I memorized that \(\sqrt{3}\) is approximately 1.7) =
~68,000 => answer is B

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Re: (4.8*10^9)^1/2 is closest in value to [#permalink]

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New post 20 Dec 2017, 07:44
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ske wrote:
\(\sqrt{4.8*10^9}\) is closest in value to

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


√(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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Re: (4.8*10^9)^1/2 is closest in value to   [#permalink] 20 Dec 2017, 07:44
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