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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 18 Oct 2015, 12:30
2
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (00:48) correct 23% (00:59) wrong based on 1065 sessions

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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, 13:35
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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 18 Oct 2015, 12:36
rewrite everything as

(48*10^8)^1/2
we get 48^1/2 * 10^4
48^1/2 is 4*sqrt(3) which is ~6.8
6.8 * 10^4 = aprox 68k
the only closest answer we have is 70k, which should be the correct answer choice.
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Re: (4.8*10^9)^(1/2) is closest in value to  [#permalink]

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New post 18 Oct 2015, 12:40
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.


(4.8*10^9)^(1/2) = (16*3*10^8) ^(1/2) = 4*10^4*3^(1/2) = 70,000

=> Ans: 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, 13:28
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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Re: (4.8*10^9)^(1/2) is closest in value to  [#permalink]

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New post 18 Oct 2015, 21:06
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.



\(\sqrt{4.8*10^9}\)
\(\sqrt{48*10^8}\)
~~\(\sqrt{49*10^8}\)
~~\(7*10^4\)
~~\(70000\)
B
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Re: (4.8*10^9)^(1/2) is closest in value to  [#permalink]

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New post 18 Oct 2015, 21:36
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.


\(\sqrt{4.8*10^9}\)
= \(\sqrt{48*10^8}\)
= \(\sqrt{48} * 10^4\)
= (approx) \(7 * 10000\)
= 70,000

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

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New post 02 May 2016, 14:59
Using some critical thinking here, we know that √4.8*10^9 = √48*10^8 = (√48) * 10^4

(√48) * 10^4 is (√16*3)*10^4
4√3 is a little less than 4*2, so you know from looking at the answers it's either B or D
Since it's 10^4, just count zeros, and you have B
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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, 04:20
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 11 Nov 2017, 08:55
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, 09:03
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Top Contributor
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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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