Square root of 2

The square root of 2 (approximately 1.4142) is the positive <a href="/facts/Real_number/R02gw5Pb">real number</a> that, when multiplied by itself or squared, equals the <a href="/facts/Number_2/u5WC44t9">number 2</a>. It may be written as 
 
 
 
 
 
 2
 
 
 
 
 {\displaystyle {\sqrt {2}}}
 
 or 
 
 
 
 
 2
 
 1
 
 /
 
 2
 
 
 
 
 {\displaystyle 2^{1/2}}
 
. It is an <a href="/facts/Algebraic_number/MkH1PzTK">algebraic number</a>, and therefore not a <a href="/facts/Transcendental_number/IrB7JppM">transcendental number</a>. Technically, it should be called the principal <a href="/facts/Square_root/AfrzfBdQ">square root</a> 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 <a href="/facts/Unit_square/6aJUASbv">square with sides of one unit of length</a>; this follows from the <a href="/facts/Pythagorean_theorem/Lh6x2Kr5">Pythagorean theorem</a>. It was probably the first number known to be <a href="/facts/Irrational_number/Psv19TET">irrational</a>. The fraction ⁠99/70⁠ (≈ 1.4142857) is sometimes used as a good <a href="/facts/Diophantine_approximation/WGVMuWF4">rational approximation</a> with a reasonably small <a href="/facts/Denominator/ghnQE9B3">denominator</a>.
Sequence A002193 in the <a href="/facts/On-Line_Encyclopedia_of_Integer_Sequences/yow6cVsU">On-Line Encyclopedia of Integer Sequences</a> consists of the digits in the <a href="/facts/Decimal_expansion/HCLBt4UQ">decimal expansion</a> of the square root of 2, here truncated to 60 decimal places:

1.414213562373095048801688724209698078569671875376948073176679

Square root of 2 open-in-new

Square root of 2