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The diagonal of a unit square
1 1 √2 1² + 1² = (√2)²
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Rational approximations to √2

Convergents of square root of 2 from continued fraction

BruchDezimalzahlFehler
1/11,0000,41421
3/21,5000,08579
7/51,4000,01421
17/121,416670,00246
99/701,414290,0000849
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Spiral of Theodorus: building every square root from unit triangles
√1=1 √2 √3 √4=2 √5 √6 √7 √8 √9=3 √10 √11 √12 √13 √14 √15 √16=4 √17 Each new hypotenuse = √(n+1). The spiral never closes.

Each right triangle has one leg equal to the previous hypotenuse and one leg equal to 1. The hypotenuses are √1, √2, √3, √4, √5… Most are irrational. √2 (red) was the first proved irrational, by the Pythagoreans around 500 BC.

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Want to test your knowledge?
Question
Apakah sqrt(2) aljabar atau transendental?
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1 / 10
Hasilkan digit Akar Kuadrat dari 2
√2 has no final digit

Akar Kuadrat dari 2 is irrational. Its decimal expansion never ends and never repeats. Every digit shown below is computed from the pecahan berlanjut.

√2 = 1 + 1/(2 + 1/(2 + 1/(2 + ...)))