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The expression "sqrt(2) * sqrt(2)" represents the product of the square root of 2 multiplied by itself. In mathematical notation, it is written as √2 × √2. This expression is a fundamental example in algebra and arithmetic, often used to illustrate properties of square roots and exponents.

The square root of 2 (√2) is an irrational number, meaning it cannot be expressed as a simple fraction and its decimal representation is non-terminating and non-repeating. Its approximate value is 1.414213562373095..., though this is only a truncated form of its infinite decimal expansion. When √2 is multiplied by itself, the result simplifies using the property of square roots that states √a × √a = a. Therefore, √2 × √2 equals 2.

This simplification can also be derived using exponent rules, where square roots are expressed as fractional exponents. Specifically, √2 is equivalent to 2^(1/2). Multiplying two such terms yields (2^(1/2)) × (2^(1/2)) = 2^((1/2) + (1/2)) = 2^1 = 2. This demonstrates the consistency of algebraic properties across different representations of mathematical operations.

The concept of √2 × √2 is often introduced in early mathematics education to reinforce understanding of square roots, exponents, and algebraic identities. It serves as a foundational example for more complex topics, such as radical expressions, polynomial multiplication, and the properties of irrational numbers.