Smallest number to be added to 900 to make a perfect  cube

We need to determine the smallest number that, when added to 900, makes the result a perfect cube.

### Steps to solve:
1. Find the cube root of 900.
   \[
   \sqrt[3]{900} \approx 9.654 
   \]
2. The nearest integers around this value are 9 and 10.

3. Calculate the cubes of both 9 and 10:
   \[
   9^3 = 729
   \]
   \[
   10^3 = 1000
   \]

4. Now, we see that:
   - \( 900 \) is greater than \( 729 \) but less than \( 1000 \).

5. To make 900 a perfect cube, we need to add enough to reach the next perfect cube, \( 1000 \).

6. The smallest number to be added:
   \[
   1000 - 900 = 100
   \]

### Conclusion:
The smallest number that must be added to 900 to make it a perfect cube is **100**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is a perfect square and how is it different from a perfect cube?
2. How can you find the cube root of any large number using estimation?
3. What are the properties of cube numbers in number theory?
4. Can the number 900 be made into a perfect square with a small addition?
5. What is the smallest number that should be subtracted from 1000 to make it a perfect cube?

**Tip**: Cube numbers grow much faster than square numbers, so when estimating, always check numbers around the cube root.

Smallest number to be added to 900 to make a perfect cube.

Discover the smallest number that needs to be added to 900 to make it a perfect cube. Learn the step-by-step process, including cube root calculations and analyzing perfect cubes like 729 and 1000. Suitable for students in Grades 6-8.

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