SQUARE-SQUARE SQUARE-SQUARE
ROOT AND ROOT AND
CUBE-CUBE ROOT CUBE-CUBE ROOT
(A) Main Concepts and Results (A) Main Concepts and Results
• 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.
• 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.