Roots: Different Base, Same Root

Which of the following is closest to $$ \frac{4}{3\pi}$$?

Incorrect. [[snippet]] When you ballpark this answer choice, you get >$$\displaystyle \sqrt{\frac{2}{3}} = \frac{\sqrt{2}}{\sqrt{3}} \approx \frac{1.4 }{1.7}$$. Expand both the numerator and denominator by 10 to see this more clearly: >$$\displaystyle \frac{1.4}{ 1.7} = \frac{14}{17}$$. This is clearly more than $$\frac{1}{2}$$ ($$\frac{1}{2} = \frac{8.5}{17}$$). Since your target is slightly smaller than 0.5, check the other answer choices for a closer match.

Incorrect. [[snippet]] When you ballpark this answer choice, you get >$$\sqrt{3} -1 \approx 1.7-1 = 0.7$$. This answer choice is greater than 0.5. Since your target is slightly _smaller_ than 0.5, check the other answer choices for a closer match.

Correct. [[snippet]] When you ballpark this answer choice, you get >$$\sqrt{2} -1 \approx 1.4-1 = 0.4$$. This is slightly smaller than 0.5. All other answer choices are not in the right __Ballpark__, so this is the right answer choice.

$$\sqrt{2}-1$$

$$\sqrt{3} - 1$$

$$\sqrt{\frac{2}{3}}$$