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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 Updated on: 14 Sep 2015, 06:22
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Question Stats:

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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

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Originally posted by ske on 14 Sep 2015, 06:07.
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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(4.8*10^9)^1/2 is closest in value to  [#permalink]

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New post 24 Feb 2018, 03:37
anudeep133 wrote:
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



hello niks18 :) its weekend the weather is awesome, but still i need to ppractice a few quant questions :) can you please help :)

How mathematically do we call the process when from this \(\sqrt{4.8*10^9}\) we get this \(\sqrt{49*10^8}\) ? :? I mean exponent is changed and also 4.8 turned into 48

Another question I didnt understand the process of taking square root from this \(\sqrt{10^8}\) when we get this \(10^4\) what is the principle logic when exponent 8 is turned in 4 after taking square root

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

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New post 24 Feb 2018, 04:04
1
dave13 wrote:
anudeep133 wrote:
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



hello niks18 :) its weekend the weather is awesome, but still i need to ppractice a few quant questions :) can you please help :)

How mathematically do we call the process when from this \(\sqrt{4.8*10^9}\) we get this \(\sqrt{49*10^8}\) ? :? I mean exponent is changed and also 4.8 turned into 48

Another question I didnt understand the process of taking square root from this \(\sqrt{10^8}\) when we get this \(10^4\) what is the principle logic when exponent 8 is turned in 4 after taking square root

many thanks! :)


Hi dave13

Query 1: \(4.8*10^9=4.8*10*10^8=48*10^8\)

Query 2: \(\sqrt{10^8}=\sqrt{(10^4)^2}=10^4\)

I will urge you to strengthen concepts of exponents before attempting these questions. Refer to GMAT Club free math book or any other good resource. This will help you gain more than simply understanding the solutions.
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Re: (4.8*10^9)^1/2 is closest in value to &nbs [#permalink] 24 Feb 2018, 04:04
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