1 Squares

When you multiply a number by itself exactly once, the result is called the Square of that number. In math, we write it with a small '2' at the top, called a power or exponent (x²).

2 Square Roots

A square root is the exact reverse of a square. Its symbol is √. When we find a square root, we are asking: "Which number, when multiplied by itself, gives this result?"

3 Cubes & Cube Roots

When you multiply a number by itself three times, it is called a Cube (x³). Its reverse is called a Cube Root (³√x).

4 Important Rules & Exam Tricks

Competitive exams love to ask conceptual questions that you can solve in 2 seconds if you know these rules:

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  The Even / Odd Rule The square of an Even number is always Even (4² = 16). The square of an Odd number is always Odd (3² = 9).
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  Ending Digits Trick A perfect square will NEVER end with the digits 2, 3, 7, or 8. If you see a number like 198 or 142 in an MCQ, you instantly know it's not a perfect square!
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  The Zeroes Rule When you take the square root of a number ending in zeroes, the number of zeroes gets cut in half. Example: √100 = 10 (2 zeroes become 1). √40000 = 200 (4 zeroes become 2). A perfect square must have an even number of trailing zeroes.
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  Negative Squares When you square a negative number, it becomes positive! (-5)² = (-5) × (-5) = 25. Therefore, if x² = 25, then x can be either +5 or -5.