User:Aman magical studies

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.