(√2.94)*(√1.13/∛0.03) is closest to which of the following

Question

A. 1
B. 3
C. 6
D. 20
E. 100

IanStewart · Accepted Answer

The answers are far apart, so I'd round off liberally: √2.94 * √1.13 is going to be roughly equal to √3 * √1 = √3.

To estimate the cube root of 0.03, you might notice that 1/27 > 0.03 > 1/64, so the cube root of 0.03 is between 1/3 and 1/4 (the cube roots of 1/27 and 1/64). So if our estimated numerator is √3, our estimate of the overall value of the fraction is somewhere between √3/(1/3) = 3√3 and √3/(1/4) = 4√3, and since √3 is roughly 1.7, the value of the fraction should be somewhere between 5.1 and 6.8, and only 6 makes sense from the answer choices.

rvgmat12 · Answer

(Root(3.3))/.3 (.3^3 = .027 approx 0.03)

= 1.8/.3 = 6 approx

C

ElenaFerrante · Answer

Could I request an expert to please solve this using first-order approximation, in particular for the cube root of 0.03. Many thanks in advance!

KarishmaB · Answer

The troublemaker is the cube root of .03 i.e. cube root of 3/100. 
 1.5^3 = 2.25*1.5  which is a bit above 3 since 1.5*2 = 3
 5^3 = 125

Hence cube root of 3/100 is about 1.5/5.

\sqrt{2.94} = 1.7  (approx because root 3 is 1.732)
 \sqrt{1.13} = 1  approx since it will be slightly greater than 1.

1.7 * \frac{1}{1.5/5} = \frac{1.7}{1.5} * 5  which is a bit greater than 5

Answer (C)

ManishaPrepMinds · Answer

Use Easy Benchmarks
√2.94 ~ √3 ~1.7
√1.13 ~ √1 ~ 1 
 ∛0.03 ~ 0.3 (since 0.3^3 = 0.027)

Substitute In the Expression: 
(√2.94)*(√1.13/∛0.03)
1.7 × (1/0.3)
1.7*10/3
17/3~ 5.6~ 6

Answer: C

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(√2.94)*(√1.13/∛0.03) is closest to which of the following

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(√2.94)*(√1.13/∛0.03) is closest to which of the following

Prep Toolkit

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