The least possible number which is subtacted from 1730 to make it a perfect cube is :

Options

A. 2
B. 1
C. 8
D. 7

Answer

To find the least possible number that can be subtracted from 1730 to make it a perfect cube, we can follow these steps:

### Step 1: Identify the nearest perfect cubes around 1730.
Perfect cubes are numbers that can be expressed as \( n^3 \) where \( n \) is an integer. We can find the cubes of integers around the cube root of 1730.

- The cube root of 1730 is approximately \( 11.5 \).
- Therefore, we can check the cubes of 11 and 12:
- \( 11^3 = 1331 \)
- \( 12^3 = 1728 \)

### Step 2: Calculate the difference between 1730 and the nearest perfect cubes.
Now, we will find the difference between 1730 and the perfect cubes we identified:

- For \( 12^3 = 1728 \):
\[ 1730 - 1728 = 2 \]

- For \( 11^3 = 1331 \):
\[ 1730 - 1331 = 399 \]

### Step 3: Determine the least number to subtract.
From the calculations, we see that:

- Subtracting 2 from 1730 gives us 1728, which is a perfect cube.
- Subtracting 399 gives us 1331, which is also a perfect cube, but 399 is much larger than 2.

### Conclusion:
The least possible number that can be subtracted from 1730 to make it a perfect cube is **2**.

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