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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, 07:22
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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

Originally posted by ske on 14 Sep 2015, 07:07.
Last edited by Bunuel on 14 Sep 2015, 07:22, edited 1 time in total.
Renamed the topic and edited the question.
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(4.8*10^9)^(1/2) is closest in value to  [#permalink]

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New post 18 Oct 2015, 13:30
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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, 07:29
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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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(4.8*10^9)^(1/2) is closest in value to  [#permalink]

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New post 18 Oct 2015, 14:28
1
(4.8*10^9)^1/2
=(48*10^8)^1/2
= (approx) (49*10^8)^1/2
=7*10^4
=70,000
Answer is B
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(4.8*10^9)^(1/2) is closest in value to  [#permalink]

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New post 18 Oct 2015, 14:35
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Bunuel 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

Kudos for a correct solution.


Eventually, we'll use a nice rule that says \(\sqrt{xy} = (\sqrt{x})(\sqrt{y})\)

First rewrite \(\sqrt{4.8*10^9}\)

\(\sqrt{4.8*10^9}\) = \(\sqrt{(4.8)(10^1)(10^8)}\)
= \(\sqrt{(48)(10^8)}\)
= (\(\sqrt{48}\))(\(\sqrt{10^8}\)) [applied rule from above]
≈ (\(\sqrt{49}\))(\(\sqrt{10^8}\))
≈ \((7)(10^4\))
≈ \(70,00\)0

Answer: B

ASIDE: we have a free video that covers various properties of roots - http://www.gmatprepnow.com/module/gmat- ... video/1037
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Re: (4.8*10^9)^(1/2) is closest in value to  [#permalink]

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New post 03 May 2016, 05:20
1
Bunuel 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

Kudos for a correct solution.


We are given √(4.8 x 10^9), and we need to determine the answer choice that is closest in value. We first simplify the expression by eliminating the decimal point in 4.8. To do this, we can move the decimal one place to the right to get 48 and simultaneously reduce 10^9 to 10^8. So we need to estimate √(48 x 10^8). Notice that 48 is very close to 49, which is a perfect square. Note, too, that the square root of 10^8 is easy to calculate because the exponent is now an even number. So let’s evaluate √(49 x 10^8):

√(49 x 10^8)

√(49) x √(10^8)

7 x 10^4

70,000

Thus √(4.8 x 10^9) ≈ 70,000.

Answer: 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, 20:03
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 11 Nov 2017, 09:55
GMATPrepNow wrote:
Bunuel 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

Kudos for a correct solution.


Eventually, we'll use a nice rule that says \(\sqrt{xy} = (\sqrt{x})(\sqrt{y})\)

First rewrite \(\sqrt{4.8*10^9}\)

\(\sqrt{4.8*10^9}\) = \(\sqrt{(4.8)(10^1)(10^8)}\)
= \(\sqrt{(48)(10^8)}\)
= (\(\sqrt{48}\))(\(\sqrt{10^8}\)) [applied rule from above]
≈ (\(\sqrt{49}\))(\(\sqrt{10^8}\))
≈ \((7)(10^4\))
≈ \(70,00\)0

Answer: B

ASIDE: we have a free video that covers various properties of roots - http://www.gmatprepnow.com/module/gmat- ... video/1037


Hello, how did you get 10^4 from 10^8? :?
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Re: (4.8*10^9)^(1/2) is closest in value to  [#permalink]

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New post 11 Nov 2017, 10:03
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dave13 wrote:
Hello, how did you get 10^4 from 10^8? :?


We want to find the square root of 10^8

So, what value when squared gives us 10^8?
The answer is 10^4

(10^4)(10^4) = 10^8
In other words, (10^4)² = 10^8
So, the square root of 10^8 equals 10^4

Does that help?

Cheers,
Brent
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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, 08:44
1
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]

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New post 16 Sep 2019, 08:04
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


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

\(\sqrt{4.8*10^9} = \sqrt{48 * 10^8} = 7 * 10^4 = 70,000\)

IMO B
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Re: (4.8*10^9)^(1/2) is closest in value to   [#permalink] 16 Sep 2019, 08:04
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