The least possible number which is subtacted from 1348 to make it a perfect cube is :

Options

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

Answer

To find the least possible number that must be subtracted from 1348 to make it a perfect cube, we can follow these steps:

### Step 1: Identify the nearest perfect cubes around 1348.
Perfect cubes are numbers that can be expressed as \( n^3 \) where \( n \) is an integer. We need to find the cubes of integers around the cube root of 1348.

Calculating the cube root of 1348:
\[ \sqrt[3]{1348} \approx 11.0 \]
Calculating the cubes of 11 and 12:
\[ 11^3 = 1331 \]
\[ 12^3 = 1728 \]

### Step 2: Determine which perfect cube is less than 1348.
From our calculations, we see that \( 11^3 = 1331 \) is less than 1348, while \( 12^3 = 1728 \) is greater than 1348. Therefore, the nearest perfect cube less than 1348 is 1331.

### Step 3: Calculate the difference between 1348 and the nearest perfect cube.
We need to subtract 1331 from 1348:
\[ 1348 - 1331 = 17 \]

### Step 4: Conclusion
The least possible number that must be subtracted from 1348 to make it a perfect cube is 17.

Thus, the answer is:
\[ \text{The least number to subtract is } 17. \]

---