Comprehensive Calculator Guide
This calculator checks whether a number is a perfect square or a perfect cube, and shows the nearest perfect squares below and above it. 144 is 12 × 12; 150 lies between 144 and 169; 64 is both a square and a cube.
Squares and cubes
A perfect square never ends in 2, 3, 7 or 8, and its digital root is 1, 4, 7 or 9. In prime factors, all powers are even for a square and multiples of 3 for a cube.
How to Use
- Enter a positive whole number.
- Nothing else is needed.
- Press “Check” to see whether it is a perfect square or cube and the nearest squares.
Formula Used
Perfect square: √n is whole | perfect cube: ∛n is whole
Practical Examples
- Example 1
- 150: between 144 and 169.
- Example 2
- 144 = 12².
- Example 3
- 64 = 8² = 4³.
Important Tips
- Learn squares to 400 and cubes to 1000.
- Rule out endings 2, 3, 7, 8.
- Use squares to estimate roots.
Common Mistakes to Avoid
- Assuming endings 4 or 9 mean a square.
- Confusing squares with even numbers.
- Forgetting 0 and 1.
Frequently Asked Questions
- Is 50 a square?
- No.
- Squares to 100?
- 1, 4, 9, …, 100.
- Square and cube?
- 1, 64, 729.