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Roots - Fractions

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Roots - Fractions [#permalink] New post 01 Mar 2010, 02:38
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

67% (01:22) correct 33% (00:00) wrong based on 6 sessions
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.
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Re: Roots - Fractions [#permalink] New post 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: Roots - Fractions [#permalink] New post 01 Mar 2010, 04:36
Thanks! CarriedInterest the OA is 'A'.
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Re: Roots - Fractions [#permalink] New post 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: Roots - Fractions [#permalink] New post 01 Mar 2010, 05:45
Even better bangalorian2000. Now it should take less than 1 min to arrive at the solution.. Thnks
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Re: Roots - Fractions [#permalink] New post 01 Mar 2010, 12:49
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: Roots - Fractions [#permalink] New post 02 Mar 2010, 01:13
What is the difficulty level of this question? Has to be less than 600.
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Re: Roots - Fractions [#permalink] New post 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: Roots - Fractions [#permalink] New post 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: Roots - Fractions [#permalink] New post 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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Re: Roots - Fractions [#permalink] New post 15 Mar 2010, 07:41
nickk wrote:
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.

Can you give an example the same way u did for the square root for the cube root?
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Re: Roots - Fractions   [#permalink] 15 Mar 2010, 07:41
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