- A natural number is called a perfect square if it is the square of some natural number.i.e., if m = n2, then m is a perfect square where m and n are natural numbers.
- A natural number is called a perfect cube if it is the cube of some natural number.i.e., if m = n3, then m is a perfect cube where m and n are natural numbers.
- Number obtained when a number is multiplied by itself is called the square of the number.
- Number obtained when a number is multiplied by itself three times are called cube number cube number.
- Squares and cubes of even numbers are even.
- Squares and cubes of odd numbers are odd.
- A perfect square can always be expressed as the product of pairs of prime factors.
- A perfect cube can always be expressed as the product of triplets of prime factors.
- The unit digit of a perfect square can be only 0, 1, 4, 5, 6 or 9.
- The square of a number having:

- 1 or 9 at the units place ends in1.
- 2 or 8 at the units place ends in 4.
- 3 or 7 at the units place ends in 9.
- 4 or 6 at the units place ends in 6.
- 5 at the units place ends in 5.

- There are 2n natural numbers between the squares of numbers n and n+1.
- A number ending in odd numbers of zeroes is not a perfect square.
- The sum of first n odd natural numbers is given by n2.
- Three natural numbers a, b, c are said to form a pythagorean triplet if a2 + b2 = c2.
- For every natural number m > 1, 2m, m2–1 and m2 + 1 form a pythagorean triplet.
- The square root of a number x is the number whose square is x.
- Positive square root of a number x is denoted by x .
- The cube root of a number x is the number whose cube is x.
- It is denoted by 3 x .
- Square root and cube root are the inverse operations of squares and cubes respectively.
- If a perfect square is of n digits, then its square root will have 2 n digit if n is even or 1 2 digit if n is odd.
- Cubes of the numbers ending with the digits 0, 1, 4, 5, 6 and 9 end with digits 0, 1, 4, 5, 6 and 9 respectively

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