The square root of 2, often known as root 2 or radical 2 and written as, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property.
Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. Its numerical value truncated to 65 decimal places is:
- 1.41421356237309504880168872420969807856967187537694807317667973799... (sequence A002193 in OEIS).
The quick approximation 99/70 (≈ 1.41429) for the square root of two is frequently used. Despite having a denominator of only 70, it differs from the correct value by less than 1/10,000 (approx. 7.2 × 10 -5).
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| Binary | 1.0110101000001001111... |
| Decimal | 1.4142135623730950488... |
| Hexadecimal | 1.6A09E667F3BCC908B2F... |
| Continued fraction | |
Read more about Square Root Of 2: History, Computation Algorithms, Proofs of Irrationality, Properties of The Square Root of Two, Series and Product Representations, Continued Fraction Representation, Paper Size
Famous quotes containing the words square and/or root:
“This house was designed and constructed with the freedom of stroke of a forester’s axe, without other compass and square than Nature uses.”
—Henry David Thoreau (1817–1862)
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For the springtime of her pride,
Eats the green by easy stages,
Nibbles at the root beneath
With intimidating teeth.”
—Gwendolyn Brooks (b. 1917)