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Intern  B
Joined: 31 Aug 2014
Posts: 20
(4.8*10^9)^1/2 is closest in value to  [#permalink]

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13 00:00

Difficulty:   15% (low)

Question Stats: 79% (01:03) correct 21% (01:25) wrong based on 1251 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

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 59726
(4.8*10^9)^(1/2) is closest in value to  [#permalink]

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15
$$\sqrt{4.8*10^9}$$ is closest in value to

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

$$\sqrt{4.8*10^9}=\sqrt{48*10^8}\approx {7*10^4}=70,000$$.

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Manager  Joined: 10 Aug 2015
Posts: 101
Re: (4.8*10^9)^1/2 is closest in value to  [#permalink]

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8
6
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
##### General Discussion
Manager  G
Joined: 13 Oct 2013
Posts: 132
Concentration: Strategy, Entrepreneurship
(4.8*10^9)^(1/2) is closest in value to  [#permalink]

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1
(4.8*10^9)^1/2
=(48*10^8)^1/2
= (approx) (49*10^8)^1/2
=7*10^4
=70,000
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4155
(4.8*10^9)^(1/2) is closest in value to  [#permalink]

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10
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

ASIDE: we have a free video that covers various properties of roots - http://www.gmatprepnow.com/module/gmat- ... video/1037
_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: (4.8*10^9)^(1/2) is closest in value to  [#permalink]

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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.

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# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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Intern  B
Joined: 04 Jun 2017
Posts: 7
Re: (4.8*10^9)^1/2 is closest in value to  [#permalink]

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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) =
VP  D
Joined: 09 Mar 2016
Posts: 1228
Re: (4.8*10^9)^(1/2) is closest in value to  [#permalink]

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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

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? GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4155
Re: (4.8*10^9)^(1/2) is closest in value to  [#permalink]

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1
Top Contributor
2
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?

(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
_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: (4.8*10^9)^1/2 is closest in value to  [#permalink]

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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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

SVP  D
Joined: 03 Jun 2019
Posts: 1885
Location: India
Re: (4.8*10^9)^(1/2) is closest in value to  [#permalink]

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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

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

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

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