Squares and cubes are foundational concepts in mathematics that appear everywhere from basic arithmetic to advanced calculations in competitive exams. Mastering them helps you solve problems faster, especially in quantitative aptitude sections of SSC, IBPS, RRB, UPSC, and Railway exams.What is a Square?When a number is multiplied by itself, the result is called its square. If a number is n, its square is written as n² (read as "n squared" or "n raised to the power 2").Formula: n² = n × nExample: 5² = 5 × 5 = 25The term "square" comes from geometry — the area of a square with side n equals n². So a square with sides of 5 units has an area of 25 square units.What is a Cube?When a number is multiplied by itself three times, the result is its cube. If a number is n, its cube is written as n³ (read as "n cubed" or "n raised to the power 3").Formula: n³ = n × n × nExample: 4³ = 4 × 4 × 4 = 64The term "cube" also comes from geometry — the volume of a cube with edge n equals n³. A cube with edges of 4 units has a volume of 64 cubic units.Perfect Squares and Perfect CubesA perfect square is a number that is the square of an integer (for example, 1, 4, 9, 16, 25). A perfect cube is a number …
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