Question

select the correct answer from each drop-down menu. the number 312 lies between the perfect cubes. so the cube root of 312 lies between the numbers, which means the cube root of 312 is most likely number. reset next

Explanation:

Step1: Find perfect cubes around 312

We know that \(6^3 = 216\) and \(7^3=343\). Since \(216<312<343\).

Step2: Determine the range of cube - root

If \(a^3 < N < b^3\), then \(a<\sqrt[3]{N}

Step3: Classify the number type

Since \(312\) is not a perfect cube (\(6^3=216
eq312\) and \(7^3 = 343
eq312\)), \(\sqrt[3]{312}\) is an irrational number.

Answer:

The number 312 lies between the perfect cubes \(216\) and \(343\). So the cube root of 312 lies between the numbers \(6\) and \(7\), which means the cube root of 312 is most likely an irrational number.