Kvadratinė šaknis

Kvadratinės šaknies funkcijos realiųjų skaičių aibėje apibrėžimo ir reikšmių sritis – neneigiamų realiųjų skaičių aibė arba intervalas ${\displaystyle \left[0,\infty \right)}$.

Kvadratinės šaknies funkcija argumentui x užrašoma taip:

${\displaystyle f(x)={\sqrt {x}}}$

Kvadratinės šaknies funkcija yra tolydi visiems neneigiamiems x ir diferencijuojama visiems teigiamiems x. Jei f žymi kvadratinės šaknies funkciją, tada jos išvestinė yra:

${\displaystyle f'(x)={\frac {1}{2{\sqrt {x}}}}.}$

Savybės

Šios kvadratinės šaknies funkcijos savybės galioja visiems realiesiems skaičiams x ir y:

1. ${\displaystyle {\sqrt {x}}=x^{\frac {1}{2}}}$
2. ${\displaystyle {\sqrt {x^{2}}}=\left|x\right|,\ \forall x\in \mathbb {R} }$
3. ${\displaystyle {\sqrt {xy}}={\sqrt {x}}{\sqrt {y}}}$
4. ${\displaystyle {\sqrt {\frac {x}{y}}}={\frac {\sqrt {x}}{\sqrt {y}}}}$ (kai y > 0)
5. ${\displaystyle {\sqrt {x^{2}}}=|x|}$

${\displaystyle {\sqrt {1\ }}=1}$	${\displaystyle {\sqrt {11}}\approx 3,\!3166}$	${\displaystyle {\sqrt {21}}\approx 4,\!5826}$	${\displaystyle {\sqrt {31}}\approx 5,\!5678}$	${\displaystyle {\sqrt {41}}\approx 6,\!4031}$
${\displaystyle {\sqrt {2\ }}\approx 1,\!4142}$	${\displaystyle {\sqrt {12}}\approx 3,\!4641}$	${\displaystyle {\sqrt {22}}\approx 4,\!6904}$	${\displaystyle {\sqrt {32}}\approx 5,\!6569}$	${\displaystyle {\sqrt {42}}\approx 6,\!4807}$
${\displaystyle {\sqrt {3\ }}\approx 1,\!7321}$	${\displaystyle {\sqrt {13}}\approx 3,\!6056}$	${\displaystyle {\sqrt {23}}\approx 4,\!7958}$	${\displaystyle {\sqrt {33}}\approx 5,\!7446}$	${\displaystyle {\sqrt {43}}\approx 6,\!5574}$
${\displaystyle {\sqrt {4\ }}=2}$	${\displaystyle {\sqrt {14}}\approx 3,\!7417}$	${\displaystyle {\sqrt {24}}\approx 4,\!8990}$	${\displaystyle {\sqrt {34}}\approx 5,\!8310}$	${\displaystyle {\sqrt {44}}\approx 6,\!6332}$
${\displaystyle {\sqrt {5\ }}\approx 2,\!2361}$	${\displaystyle {\sqrt {15}}\approx 3,\!8730}$	${\displaystyle {\sqrt {25}}=5}$	${\displaystyle {\sqrt {35}}\approx 5,\!9161}$	${\displaystyle {\sqrt {45}}\approx 6,\!7082}$
${\displaystyle {\sqrt {6\ }}\approx 2,\!4495}$	${\displaystyle {\sqrt {16}}=4}$	${\displaystyle {\sqrt {26}}\approx 5,\!0990}$	${\displaystyle {\sqrt {36}}=6}$	${\displaystyle {\sqrt {46}}\approx 6,\!7823}$
${\displaystyle {\sqrt {7\ }}\approx 2,\!6458}$	${\displaystyle {\sqrt {17}}\approx 4,\!1231}$	${\displaystyle {\sqrt {27}}\approx 5,\!1962}$	${\displaystyle {\sqrt {37}}\approx 6,\!0828}$	${\displaystyle {\sqrt {47}}\approx 6,\!8557}$
${\displaystyle {\sqrt {8\ }}\approx 2,\!8284}$	${\displaystyle {\sqrt {18}}\approx 4,\!2426}$	${\displaystyle {\sqrt {28}}\approx 5,\!2915}$	${\displaystyle {\sqrt {38}}\approx 6,\!1644}$	${\displaystyle {\sqrt {48}}\approx 6,\!9282}$
${\displaystyle {\sqrt {9\ }}=3}$	${\displaystyle {\sqrt {19}}\approx 4,\!3589}$	${\displaystyle {\sqrt {29}}\approx 5,\!3852}$	${\displaystyle {\sqrt {39}}\approx 6,\!2450}$	${\displaystyle {\sqrt {49}}=7}$
${\displaystyle {\sqrt {10\ }}\approx 3,\!1623}$	${\displaystyle {\sqrt {20\ }}\approx 4,\!4721}$	${\displaystyle {\sqrt {30\ }}\approx 5,\!4772}$	${\displaystyle {\sqrt {40\ }}\approx 6,\!3246}$	${\displaystyle {\sqrt {50\ }}\approx 7,\!0710}$