01. Introduction
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Square of a number: The product of a number multiplied by itself.
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Square root of a number: The value which, when multiplied by itself, gives the original number.
Key Concept:
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Squaring and finding the square root are inverse operations.
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Only non-negative numbers have real square roots (for basic arithmetic).
2. Properties of Squares
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Square of positive numbers is positive.
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Square of negative numbers is also positive.
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Zero squared is zero.
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Squares grow rapidly as the number increases.
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Squares are useful in geometry, algebra, and Pythagoras theorem applications.
3. Properties of Square Roots
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Non-negative: Square roots are non-negative for real numbers.
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Inverse operation: Square root of a square returns the original number.
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Multiplication: The square root of a product equals the product of the square roots.
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Division: The square root of a quotient equals the quotient of the square roots.
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Square roots help in solving quadratic problems, geometry, and measurements.
4. Types of Square Roots
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Perfect Square Root:
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Numbers whose square roots are whole numbers.
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Example: 1, 4, 9, 16, 25…
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Non-Perfect Square Root:
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Numbers whose square roots are decimal or irrational numbers.
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Example: 2, 3, 5…
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5. Methods to Find Square Roots (Conceptual)
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Prime factorization method – Breaking number into prime factors.
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Estimation method – Approximate between two perfect squares.
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Repeated subtraction – For small numbers, based on odd numbers.
6. Key Points to Remember
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Square: Number × itself
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Square root: Number whose square gives the original number
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Squares are always non-negative
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Square roots are inverse of squares
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Useful in algebra, geometry, and real-life calculations
