Table of Contents
- 1 What number is both a perfect square and a perfect cube?
- 2 What is the smallest number which is a perfect square and a perfect cube?
- 3 What is the smallest integer which becomes a two digit integer when squared?
- 4 Which is the smallest three digit perfect cube?
- 5 How do you know if a number is a perfect cube?
- 6 Is 3^6 a perfect square or an odd cube?
What number is both a perfect square and a perfect cube?
There are 3 cubes which are also square numbers, but only 729 is a three digit number. The next would be 46=4096=163=642 a four-digit number. Note that 1,4and9 are the first three square numbers, Their cubes are therefore both squares and cubes.
What is the smallest number which is a perfect square and a perfect cube?
64 is the smallest perfect square as well as the perfect cube, because 82 = 64 43 = 64. Hope this helps.
Is 21 a perfect square or perfect cube?
List of Perfect Cubes 1 to 50
Number (x) | Multiplied Three times by itself | Cubes (x3) |
---|---|---|
18 | 18× 18× 18 | 5832 |
19 | 19× 19× 19 | 6859 |
20 | 20× 20× 20 | 8000 |
21 | 21× 21× 21 | 9261 |
What is the smallest integer which becomes a two digit integer when squared?
The answer must be a⁶ for some integer a due to the properties of exponentiation.
Which is the smallest three digit perfect cube?
729 is the smallest 3 digit number perfect cube.
What is the smallest number that is perfect square as well?
The smallest number that is perfect square as well perfect cube, obviously is 1 but this is not less than 10. The next number that’s perfect square as well as perfect cube is 64 butthis is not an odd number.
How do you know if a number is a perfect cube?
If a number has a property of being both a perfect square and a perfect cube then it must be a perfect 6 th power. 1 6 = 1 which is a square and a cube 2 6 = 64 which is a square and a cube 3 6 = 729 which is a square and a cube
Is 3^6 a perfect square or an odd cube?
For a number to be both a perfect square and a perfect cube, it must be the sixth power of some base; for that number to be odd, the base must be odd. Since 1 as the base won’t do (1^6 = 1 < 10), the base must be 3, whence 3^6 = 729 = 27^2 = 9^3.
How many perfect squares are there in 64 and 729?
Answers: 64 which is 8 squared and 4 cubed. 729 which is 27 squared and 9 cubed. If a number has a property of being both a perfect square and a perfect cube then it must be a perfect 6 th power.