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Of the following, which is the best approximation to 0.0026^1/2 ?

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Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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01 Mar 2010, 02:38
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Of the following, which is the best approximation to $$\sqrt{0.0026}$$?

(A) 0.05
(B) 0.06
(C) 0.16
(D) 0.5
(E) 0.6
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Dec 2014, 01:35, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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01 Mar 2010, 03:03
abhi758 wrote:
Of the following, which is the best approximation to $$\sqrt{0.0026}$$?
(A) 0.05
(B) 0.06
(C) 0.16
(D) 0.5
(E) 0.6

Kindly provide the steps to the solution. OA to be posted soon.

SQRT .0026 =
SQRT (26 x 10^-4) =
SQRT 26 x SQRT (10^-4) =
(approx.) 5*10^(-4/2) =
5*10^-2 =
.05

A

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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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01 Mar 2010, 05:17
abhi758 wrote:
Of the following, which is the best approximation to $$\sqrt{0.0026}$$?
(A) 0.05
(B) 0.06
(C) 0.16
(D) 0.5
(E) 0.6

Kindly provide the steps to the solution. OA to be posted soon.

Backsolving 0.05^2 = .0025 it is nearest to .0026 hence A.

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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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01 Mar 2010, 12:49
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When you have square or cubed roots of numbers that are less than 0 you can use the following.
For square roots:

Square root the number at the end of the decimal (so if it were (0.0026)^0.5, you would square root 26) and divide the number of decimal places by 2. In this case, we know that the square root of 26 is a tiny bit more than 5, and dividing the number of decimal places (4) by 2 gives you 2 decimal places. Thus the answer is approximately 0.05

Cube root of a number: same procedure as above, but we cube root the number at the end of the fraction and divide the number of decimal places by 3.

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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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06 Mar 2010, 09:55
abhi758 wrote:
Of the following, which is the best approximation to $$\sqrt{0.0026}$$?
(A) 0.05
(B) 0.06
(C) 0.16
(D) 0.5
(E) 0.6

Kindly provide the steps to the solution. OA to be posted soon.

Square root of a number that has four digits to the right of decimal would have two digits to the right of decimals in the solution. So by this we rule out option D & E

Now the approx value of (26)^1/2 would be 5. The solution would therefore be A.

Hope this helps.
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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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06 Mar 2010, 15:48
this is how I did it....
nearest to 26 is 25..root of this is 5
therefore, btw a) and d)
with 2 zeros before the decimal point, I took .05*.05 = 0.0025

so it is A...interesting one

HTH

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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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11 Mar 2010, 06:20
I used scientific notation.

\sqrt{26*10^-4}

\sqrt{26}close to square root of 5 (25) ... 10^-4 becomes 10^-2 and ans is 0.05.

A.

Make sense?
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05 Jul 2011, 23:48
Take the square of A, B, and C then take the 4th power of D and E. The closest is A or .0025.

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05 Jul 2011, 23:56
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Expert's post
ssarkar wrote:
Of the following, which is the best approximation to sq root 0.0026 ?
(A) 0.05
(B) 0.06
(C) 0.16
(D) 0.5
(E) 0.6

0.0026 = 26/10,000

We want to estimate the square root of this, so we can round off the numerator to the closest perfect square, which is 25. Thus

$$\sqrt{ \frac{26}{10,000} } \approx \sqrt{ \frac{25}{10,000} } = \frac{ \sqrt{25} }{ \sqrt{10,000} } = \frac{5}{100} = 0.05$$
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06 Jul 2011, 19:33
= sqrt(26*10^-4)

= (10^-2)*sqrt(26)

ie approximately 0.05

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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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25 Dec 2014, 01:37
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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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22 Aug 2016, 11:19
Expert's post
Top Contributor
abhi758 wrote:
Of the following, which is the best approximation to $$\sqrt{0.0026}$$?

(A) 0.05
(B) 0.06
(C) 0.16
(D) 0.5
(E) 0.6

√0.0026 = √(26/10000)
= (√26)/(√10000)
≈ 5/100
≈ 0.05

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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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Re: Of the following, which is the best approximation to 0.0026^1/2 ? [#permalink]

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24 Oct 2017, 05:42
abhi758 wrote:
Of the following, which is the best approximation to $$\sqrt{0.0026}$$?

(A) 0.05
(B) 0.06
(C) 0.16
(D) 0.5
(E) 0.6

Since 0.05^2 = 0.0025 and 0.06^2 = 0.0036, we see that √0.0026 is between 0.05 and 0.06. However, since 0.0026 is closer to 0.0025 than it is to 0.0036, √0.0026 is closest to 0.05.

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Re: Of the following, which is the best approximation to 0.0026^1/2 ?   [#permalink] 24 Oct 2017, 05:42
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