The least positive number which is subtracted from 1369 to make it a perfect cube is:

Options

A. 17
B. 38
C. 34
D. None of these

Answer

To find the least positive number that needs to be subtracted from 1369 to make it a perfect cube, follow these steps:

### Step 1: Identify the nearest perfect cubes
We start by identifying the perfect cubes around the number 1369. The cubes of integers are:
- \(10^3 = 1000\)
- \(11^3 = 1331\)
- \(12^3 = 1728\)

From this, we can see that \(1369\) lies between \(11^3\) (1331) and \(12^3\) (1728).

### Step 2: Determine the nearest perfect cube
Since \(1369\) is closer to \(1331\) than to \(1728\), we will consider \(1331\) as the nearest perfect cube.

### Step 3: Calculate the difference
Next, we need to find out how much we need to subtract from \(1369\) to reach \(1331\):
\[ 1369 - 1331 = 38 \]

### Step 4: Conclusion
Thus, the least positive number that needs to be subtracted from \(1369\) to make it a perfect cube is \(38\).

### Final Answer
The answer is \(38\).

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