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

Question

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

IanStewart · Accepted Answer

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

nickk · Answer

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.

carriedinterest · Answer

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

A

bangalorian2000 · Answer

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

mustdoit · Answer

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.

amma4u · Answer

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

TheSituation · Answer

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?

Venchman · Answer

Take the square of A, B, and C then take the 4th power of D and E. The closest is A or .0025.

Spidy001 · Answer

= sqrt(26*10^-4)

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

ie approximately 0.05

Answer is A.

Bunuel · Answer

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BrentGMATPrepNow · Answer

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

ScottTargetTestPrep · Answer

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.

Answer: A

matchatea · Answer

\sqrt{ 0.0026 } is 26 x  10^-4 .
So its \sqrt{26} X  10^-2 .
Since \sqrt{25}is 5, \sqrt{26} is greater than 5. 
Hence by approximation A is correct answer

JLambert · Answer

When multiplying two decimals, disregard the decimal and just multiply as normal. Then, count how many places come after those original decimals and add them back in. It's part of the reason you can tell that multiplying decimals makes them smaller.

6^2 = 36 and 5^2 = 25, so it's probably A or D. From there, I can count four digits to the right of the decimal. So, I'm looking for an answer that has two digits to the right (that way is also two digits when I multiply it together). Not the heaviest way compared to some of the other answers, but it might help someone who thinks like me.

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 ?

Prep Toolkit

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