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Intern  B
Joined: 31 Aug 2014
Posts: 21
(4.8*10^9)^1/2 is closest in value to  [#permalink]

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8
7 00:00

Difficulty:   15% (low)

Question Stats: 75% (01:03) correct 25% (01:16) wrong based on 272 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

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Please press+ 1kudos if you appreciate this post and for motivation !!

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.
##### Most Helpful Community Reply
Manager  Joined: 10 Aug 2015
Posts: 103
Re: (4.8*10^9)^1/2 is closest in value to  [#permalink]

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7
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
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) =
~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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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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(4.8*10^9)^1/2 is closest in value to  [#permalink]

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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! Retired Moderator D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
Re: (4.8*10^9)^1/2 is closest in value to  [#permalink]

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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.
Non-Human User Joined: 09 Sep 2013
Posts: 11002
Re: (4.8*10^9)^1/2 is closest in value to  [#permalink]

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_________________ Re: (4.8*10^9)^1/2 is closest in value to   [#permalink] 24 Mar 2019, 12:19
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