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What is the square root of 5?

The square root of 5, denoted as √5, is an irrational number.

  • Value: Its approximate decimal value is 2.23606797749979...

  • Irrationality: It's an example of an algebraic irrational number. This means it cannot be expressed as a simple fraction a/b, where a and b are integers.

  • Applications: The square root of 5 appears in several areas of mathematics:

    • Golden Ratio: It is related to the golden ratio (φ), specifically φ = (1 + √5)/2 ≈ 1.618.

    • Fibonacci Sequence: It's used in Binet's formula, which gives the n-th term of the Fibonacci sequence.

    • Geometry: It can appear in the side lengths of certain geometric figures.

  • Continued Fraction: The square root of 5 has a simple continued fraction representation: [2; 4, 4, 4, ...].

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