Which of the following is the best approximation of

Question

Which of the following is the best approximation of  \sqrt{3.8*10^{25}} ?

A. 1.9*10^5

B. 6.2*10^5

C. 1.9*10^12

D. 6.2*10^12

E. 1.9*10^25

Bunuel · Accepted Answer

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Detran · Answer

Sometimes its best to turn a decimal into a whole number. If you change it to 38 x 10^24 you can bring of the ten to the 24 as 10^12.

the square root of 38 is going to be a little bit bigger than 6. since 6 x 6 = 36.

so the closest answer here is D

AlexGenkins1234 · Answer

Lets' denote the inside of the root with 'original tag ('original'=3.8*10^{25})
notice that: 
- 3.8*10^{25}=38*10^{24}
- 38*10^{24}<49*10^{24}

\sqrt{36*10^{24}}<\sqrt{'original'}<\sqrt{49*10^{24}}

so we get

6*10^{24}<'original'<7*10^{24}

and from here we can see the answer

mvictor · Answer

first of all, sqrt(x^25) is not x^5. it can be rewritten as: x^(25/2)
A, B, and E can be eliminated right away.

now..take one factor of 10 and multiply by 3.8. we got 38*10^24.
10^24 under radical is 10^2. 
38 squared is slightly more than 6.

D

JeffTargetTestPrep · Answer

We want the exponent of the 10 to be an even number, because taking the square root is easier if the exponent is even. Let’s simplify the given equation:

√(3.8 x 10^25) = √(38 x 10^24) = √38 x √10^24 = √38 x 10^12 ≈ 6.2 x 10^12

Answer: D

energetics · Answer

√(3.8*10^25)

√(38) * √(10^24)

Estimate, √(36) = 6, thus our number is slightly more * 10^12, D.

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