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.
Similar Questions
- Find the smallest natural number N such that the product $288 \times N$ is a perfect cube.
- Find the least number by which 6250 should be multiplied, so that it becomes a perfect cube.
- The square root of 18769 consists of how many digits?
- The square root of $1\frac{11}{25}$ is:
Evaluate \(21^3 + (-2)^3 + (-19)^3\)
- The cube root of 150 will lie between:
- Find the product of square root of 16 and square of 4?
- The value of $\sqrt{142884}$ is:
- The number by which 62557 can be divided to make it a perfect cube is:
- What is the value of $99^3$?
Important Questions from Cube and Cube Root
- Find the smallest natural number N such that the product $288 \times N$ is a perfect cube.
- Find the least number by which 6250 should be multiplied, so that it becomes a perfect cube.
- The square root of 18769 consists of how many digits?
- The square root of $1\frac{11}{25}$ is:
Two different positions of the same dice are shown, the six face of which are numbered from 1 to 6. Select the number that will be on the face opposite to the face having the number '3'.
