what should be added to 2714 to make the sum a perfect cube?

Options

A. 10
B. 517
C. 30
D. 150

Answer

To find out what should be added to 2714 to make the sum a perfect cube, we can follow these steps:

### Step 1: Identify the nearest perfect cubes
First, we need to find the nearest perfect cubes around 2714. The perfect cubes are numbers like \(1^3\), \(2^3\), \(3^3\), etc.

Calculating the cubes of integers:
- \(13^3 = 2197\)
- \(14^3 = 2744\)

### Step 2: Determine the nearest perfect cube
From the calculations, we see that:
- \(2197\) is less than \(2714\) (13th cube)
- \(2744\) is greater than \(2714\) (14th cube)

### Step 3: Calculate the difference
Now, we need to find out how much we need to add to \(2714\) to reach the next perfect cube, which is \(2744\).

\[ \text{Difference} = 2744 - 2714 = 30 \]

### Step 4: Conclusion
Thus, we need to add \(30\) to \(2714\) to make it a perfect cube.

### Final Answer
The number that should be added to \(2714\) to make the sum a perfect cube is **30**.

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