Noo fraue
Ayns [[maddaght]], ta'n '''{{mvar|n}}oo fraue''', ny yn '''{{mvar|n}}-oo fraue''', jeh [[earroo]] {{mvar|x}} çheet er earroo {{mvar|r}} (yn raue) quoi, tra t'eh [[assponentaghey|yrjit dys pooar]] y [[slane-earroo jarrooagh|clane-earroo jarrooagh]] {{mvar|n}}, cur magh&nbsp;{{mvar|x}}: <math display="block">r^n = \underbrace{r \times r \times \cdots \times r}_{n\text{ keayrtyn}} = x.</math>

Ta'n slane-earroo {{mvar|n}} enmyssit yn ''ayndagh'' ny yn ''cheim'', as ta'n earroo {{mvar|x}}, quoi ta'n raue goit ass, enmssit y ''radicand.'' Ta fraue jeh'n 2h cheim enmyssit ''[[fraue cherrinagh]]'' as ta fraue jeh 3oo keimyn enmyssit ''[[fraue chioobagh]]''. Ta co-earrooaghey jeh'n {{mvar|n}}oo fraue enmyssit '''tayrn magh fraue'''.

Myr sampleyr, she fraue cherrinagh jeh {{math|9}} eh {{math|3}}, er-yn-oyr dy vel {{math|1=3{{sup|2}} = 9}}, as she fraue cherrinagh jeh {{math|9}} eh {{math|−3}} chammah, er-yn-oyr dy vel {{math|1=(−3){{sup|2}} = 9}}.

Ta'n {{mvar|n}}oo fraue jeh {{mvar|x}} screeuit myr <math>\sqrt[n]{x}</math> lesh ymmyd y [[cowrey fraueoil|chowrey fraueoil]] ny yn ''bun-earroo'' <math>\sqrt{\phantom x}</math>. Er y chooid smoo, ta'n raue cherrinagh screeuit gyn yn {{mvar|n}} myr {{tmath|\sqrt x}} ny lomarcan. Ta goaill yn ''n''oo fraue jeh earroo coontit myr yn obbreeaght [[curmeyder contraartagh#Curmeyderyn kerrinaghey as fraueyn kerrinagh|chontraartagh]] jeh'n [[assponentaghey]],<ref>{{cite web |url=https://www.nagwa.com/en/explainers/985195836913 |access-date=22 Jerrey Souree 2023 |title=Lesson Explainer: nth Roots: Integers}}</ref> as foddee eh ve screeuit myr assponent [[Corrillagh (maddaght)|corrillaghoil]]:

<math display="block">\sqrt[n]{x} = x^{1/n}.</math>

Da feer earroo jarrooagh {{mvar|x}}, ta <math>\sqrt{x}</math> cowraghey yn raue cherrinagh yarrooagh jeh {{mvar|x}} as ta <math>\sqrt[n]{x}</math> cowraghey yn {{mvar|n}}oo eer raue yarrooagh. Cha nel fraueyn kerrinagh lesh feer-leaghyn ec feer earroo jiooldagh {{math|−''x''}}, agh tra ta {{mvar|x}} ny earroo conrieugh ta daa raue cherrinagh [[earroo neurieugh|neurieugh]], {{tmath|+i\sqrt x }} as {{tmath|-i\sqrt x }}, raad she {{mvar|i}} yn [[unnid neurieugh]].

Er y chooid smoo, ta {{mvar|n}} {{mvar|n}}oo fraueyn er-lheh lesh leaghyn conrieugh ec [[earroo conrieugh]] neu-neunhee, skeaylt mygeayrt kiarkyl conrieugh er [[slane-leagh#Earrooyn conrieugh|slane-leagh]]. (She neunhee lesh [[yl-raue|yl-raght]] {{mvar|n}} eh yn {{mvar|n}}oo fraue jeh {{math|0}}, as ta'n kiarkyl shen jee-ghiennaghtyn dys poynt.) Myr shen, foddee-shiu coontey tayrn magh ny {{mvar|n}}oo fraueyn jeh earroo conrieugh {{mvar|x}} myr [[curmeyder yl-leaghit]]. Rere cliaghtey, ta'n [[bun-leagh]] jeh'n churmeyder shen, ta enmyssit y '''vun-raue''' as cowrit lesh {{tmath|\sqrt[n]{x} }}, coontit myr yn {{mvar|n}}oo fraue lesh yn eer ayrn smoo as 'sy chooish er-lheh tra ta {{mvar|x}} ny eer earroo jiooldagh, yn fer lesh [[ayrn neurieugh]] jarrooagh. She feer earroo jarrooagh eh bun-raue jeh feer earroo jarrooagh chammah. Myr [[curmeyder (maddaght)|curmeyder]], [[curmeyder kinjagh|s'kinjagh]] y vun-raue 'sy [[plaaney conrieugh|phlaaney conrieugh]], faagail magh liorish yn eer essyl jiooldagh.

Ta '''surdey''' ny '''fraueoilagh''' çheet er earroo erbee lesh fraue neuresoonagh, goaill stiagh adsyn lesh y chowrey fraueoil er lheh. Ta dreagh ta goaill stiagh fraueoilagh, gyn scansh e staydys myr fraue cherrinagh, fraue chioobagh, ny fraue ny s'yrjey, enmyssit '''dreagh draueoilagh''', as mannagh vel [[curmeyder tarcheimneeoil|curmeyderyn tarcheimneeoil]] ny [[earroo tarcheimneeoil|earrooyn tarcheimneeoil]] echey t'eh enmyssit ''[[dreagh algeeragh]]''.

==Imraaghyn==
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{{DISPLAYTITLE:{{mvar|n}}oo fraue}}

[[Ronney:Algeerey bunneydagh]]
[[Ronney:Obbreeaghtyn er earrooyn]]
Ayns maddaght, ta'n oo fraue, ny yn -oo fraue, jeh earroo  çheet er earroo  (yn raue) quoi, tra t'eh yrjit dys pooar y clane-earroo jarrooagh , cur magh : 

Ta'n slane-earroo  enmyssit yn ayndagh ny yn cheim, as ta'n earroo , quoi ta'n raue goit ass, enmssit y radicand. Ta fraue jeh'n 2h cheim enmyssit fraue cherrinagh as ta fraue jeh 3oo keimyn enmyssit fraue chioobagh. Ta co-earrooaghey jeh'n oo fraue enmyssit tayrn magh fraue.

Myr sampleyr, she fraue cherrinagh jeh  eh , er-yn-oyr dy vel , as she fraue cherrinagh jeh  eh  chammah, er-yn-oyr dy vel .

Ta'n oo fraue jeh  screeuit myr  lesh ymmyd y chowrey fraueoil ny yn bun-earroo . Er y chooid smoo, ta'n raue cherrinagh screeuit gyn yn  myr  ny lomarcan. Ta goaill yn noo fraue jeh earroo coontit myr yn obbreeaght chontraartagh jeh'n assponentaghey, as foddee eh ve screeuit myr assponent corrillaghoil:

Da feer earroo jarrooagh , ta  cowraghey yn raue cherrinagh yarrooagh jeh  as ta  cowraghey yn oo eer raue yarrooagh. Cha nel fraueyn kerrinagh lesh feer-leaghyn ec feer earroo jiooldagh , agh tra ta  ny earroo conrieugh ta daa raue cherrinagh neurieugh,  as , raad she  yn unnid neurieugh.

Er y chooid smoo, ta  oo fraueyn er-lheh lesh leaghyn conrieugh ec earroo conrieugh neu-neunhee, skeaylt mygeayrt kiarkyl conrieugh er slane-leagh. (She neunhee lesh yl-raght  eh yn oo fraue jeh , as ta'n kiarkyl shen jee-ghiennaghtyn dys poynt.) Myr shen, foddee-shiu coontey tayrn magh ny oo fraueyn jeh earroo conrieugh  myr curmeyder yl-leaghit. Rere cliaghtey, ta'n bun-leagh jeh'n churmeyder shen, ta enmyssit y vun-raue as cowrit lesh , coontit myr yn oo fraue lesh yn eer ayrn smoo as 'sy chooish er-lheh tra ta  ny eer earroo jiooldagh, yn fer lesh ayrn neurieugh jarrooagh. She feer earroo jarrooagh eh bun-raue jeh feer earroo jarrooagh chammah. Myr curmeyder, s'kinjagh y vun-raue 'sy phlaaney conrieugh, faagail magh liorish yn eer essyl jiooldagh.

Ta surdey ny fraueoilagh çheet er earroo erbee lesh fraue neuresoonagh, goaill stiagh adsyn lesh y chowrey fraueoil er lheh. Ta dreagh ta goaill stiagh fraueoilagh, gyn scansh e staydys myr fraue cherrinagh, fraue chioobagh, ny fraue ny s'yrjey, enmyssit dreagh draueoilagh, as mannagh vel curmeyderyn tarcheimneeoil ny earrooyn tarcheimneeoil echey t'eh enmyssit dreagh algeeragh.

Imraaghyn

Ronney:Algeerey bunneydagh
Ronney:Obbreeaghtyn er earrooyn