How to Identify Perfect Squares and Cubes?
After learning the definition of both perfect squares and perfect cube, we learn some easy ways for their identification. First, we learn about ‘unit digit’ or ‘end digit’ method, then we study another method prime factorization:
Unit Digit Method
Unit Digit Method is helpful in knowing about the possibility of a number being perfect square or cube without any actual test just by looking at the unit digit of a number. Let’s learn more about it.
- Squares: If a number is a perfect square, its end digit should only be 0, 1, 4, 5, 6, or 9. Any square whose unit digit is any other digit cannot be a perfect square. For example, the square of ‘7’ is ’49’. Here, 49 is a perfect square because its unit digit is ‘9’. Similarly, take the square of ’12’. The square of ’12’ is ‘144’ which is a perfect square, because its unit digit is ‘4’.
- Cubes: The unit digit of a perfect cube should only be 0, 1, 8, or 9. In this way, we can easily verify whether a number is a perfect cube or not. For example, ‘1728’ is a perfect cube because its last digit is ‘8’.
Note: There are also some exceptions. Some numbers are both a ‘perfect square’ and a ‘perfect cube’. For example, ’64’ is both perfect square and perfect cube.
Prime Factorization Method
Since, Unit digit method only gives a hint about the possibility of a number being perfect square or cube. However, the actual clarity can be gained only through prime factorization method.
- Squares: In this method, when we prime factorize any number, each group of prime factors should have an even exponent i.e. ‘multiples of 2′. For example, the given number is ’36’. Its prime factor is 22 ⨯ 32 . Each group of prime factors has an even exponent ‘2’ therefore 36 is a perfect square.
- Cubes: In this method, when we prime factorize any number, each group of prime factors should have an exponent that is multiple of ‘3’. For example, the given number is ’64’. Its prime factor is 26 . The exponent ‘6’ is multiple of ‘3’ therefore 64 is a perfect cube.
Squares and Cubes
Squares and Cubes are mathematical operations involving numbers that are essential in various areas of mathematics. Square of a number is obtained by multiplying the number by itself where as a cube of a number is obtained by multiplying the number by itself twice.
In this article, we will learn what is Square and Cube Number. We will also learn about Perfect Squares and Cube and Square and Cube charts 1 to 100.
Table of Content
- What is Square Number?
- What is Cube Number?
- Perfect Square and Cubes
- Squares and Cubes from 1 to 50
- Chart of Squares and Cubes 1 to 100
Contact Us