Square root: Difference between revisions

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The '''square root''' of a number is the value of one of two equal factors of that number. For example,

the number 16 has the factor 4, which when multiplied by itself -(ie: (4)*(4) - gives 16. Hence the square root of 16 is 4. Minus 4 (-4) is also a square root of 16, as it gives sixteen when multiplied by itself.

The square root can also be shown to be the 1/2 power of the number.

the number 16 has the factor 4, which when multiplied by itself - (4)*(4) - gives 16. Hence the square root of 16 is 4. Minus 4 (-4) is also a square root of 16, as it gives sixteen when multiplied by itself.

The square root can also be shown to be

the 1/2 power of the number.

The square root [[function]] generally maps [[rational number]]s to [[algebraic number|algebraic]] and [[constructible]] [[irrational number]]s, except in cases where the [[numerator]] and [[denominator]] are both [[perfect square]]s. It maps the [[area]] of a [[square]] to its side length.

The square root [[function]] generally maps [[rational number|rational numbers]]s to [[algebraic number|algebraic]] and [[constructible]] [[irrational number|irrational numbers]]s, except in cases where the [[numerator]] and [[denominator]] are both [[perfect square|perfect squares]]s. It also maps the [[area]] of a [[square]] to its side length.

Rapidly [[convergent]] methods for calculating [[rational]] [[approximation]]s of [[irrational]] square roots include [[Newton's method]] and [[Pell's equation]].