Find Least Integer to Subtract for Perfect Cube
The objective is to determine the smallest positive integer that must be subtracted from 2750 to obtain a perfect cube.
Step 1: Identify Perfect Cubes Near 2750
First, list the cubes of integers to find the largest perfect cube smaller than 2750.
- $13^3 = 13 \times 13 \times 13 = 2197$
- $14^3 = 14 \times 14 \times 14 = 2744$
- $15^3 = 15 \times 15 \times 15 = 3375$
Step 2: Determine the Target Perfect Cube
Comparing 2750 with the calculated cubes, we see that 2744 is the largest perfect cube less than 2750.
Step 3: Calculate the Integer to Subtract
The integer to be subtracted is the difference between 2750 and this target perfect cube (2744).
The calculation is as follows:
$2750 - 2744 = 6$
Conclusion
Therefore, the least positive integer that should be subtracted from 2750 to make the result a perfect cube is 6.
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