Question

Truncate the decimal expansion of 15 to find the best approximation. A) 2.4 < 15 < 2.5 B) 2.46 < 15 < 2.47 C) 2.46 < 15 < 2.50 D) 2.47 < 15 < 2.50

Answer 1

∛15 ≈ 2.466212...

The best choice appears to be ...
  B) 2.46 < ∛15 < 2.47

Answer 2

This is not the complete question.

In this we have to truncate the decimal expansion of $^3\sqrt{15}$ to find the best approximation. The options are:

A) 2.4 <$^3\sqrt{15}$ < 2.5

B) 2.46 < $^3\sqrt{15}$ < 2.47

C) 2.46 <$^3\sqrt{15}$ < 2.50

D) $2.47 < ^3\sqrt{15} < 2.50$

Solution: Consider the cube root of 15,

By using the calculator, we will calculate its cube root.

$^3\sqrt{15}=2.4662$

Now, we have to find the option which approximates it in the best way.

In option A. It is given between 2.4 and 2.5 which is not the best approximation as the decimal expansion is 2.46 is between 2.46 and 2.47.

In Option B: It is given between 2.46 and 2.47 which is the best approximation as the decimal expansion is between 2.46 and 2.47.

In Option C: It is given between 2.46 and 2.50 which is not the best approximation as the decimal expansion is 2.46 is between 2.46 and 2.47.

In Option D: It is given between 2.47 and 2.50 which is not the best approximation as the decimal expansion is 2.46 is between 2.46 and 2.47.

Hence, The decimal expansion of $^3\sqrt{15}$ is between 2.46 and 2.47.

So, we get 2.46 < $^3\sqrt{15}$ < 2.47

Therefore, Option B is the correct answer.