Réitigh sqrt{5}-3sqrt{20}+sqrt{125}+sqrt{1/5}

Luacháil

Tráth na gCeist

Arithmetic

5 fadhbanna cosúil le:

Fadhbanna den chineál céanna ó Chuardach Gréasáin

https://math.stackexchange.com/questions/2838072/how-to-express-frac-frac12-sqrt4-frac34-sqrt4-frac14-i

https://socratic.org/questions/how-do-you-rationalize-the-denominator-and-simplify-2sqrt12-sqrt5-sqrt5-4sqrt3

https://socratic.org/questions/how-do-you-rationalize-the-denominator-and-simplify-2sqrt-5-3sqrt-2-2sqrt-5-3sqr

https://socratic.org/questions/how-do-you-simplify-5sqrt-6-sqrt-20-2sqrt-7-sqrt-35

https://socratic.org/questions/how-do-you-order-the-following-from-least-to-greatest-sqrt-1-2-sqrt-1-3-sqrt-2-3

Roinn

Cóipeáladh go dtí an ghearrthaisce

\sqrt{5}-3\times 2\sqrt{5}+\sqrt{125}+\sqrt{\frac{1}{5}}

Fachtóirigh 20=2^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{5}. Tóg fréamh chearnach 2^{2}.

\sqrt{5}-6\sqrt{5}+\sqrt{125}+\sqrt{\frac{1}{5}}

Méadaigh -3 agus 2 chun -6 a fháil.

-5\sqrt{5}+\sqrt{125}+\sqrt{\frac{1}{5}}

Comhcheangail \sqrt{5} agus -6\sqrt{5} chun -5\sqrt{5} a fháil.

-5\sqrt{5}+5\sqrt{5}+\sqrt{\frac{1}{5}}

Fachtóirigh 125=5^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{5^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{5^{2}}\sqrt{5}. Tóg fréamh chearnach 5^{2}.

\sqrt{\frac{1}{5}}

Comhcheangail -5\sqrt{5} agus 5\sqrt{5} chun 0 a fháil.

\frac{\sqrt{1}}{\sqrt{5}}

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{1}{5}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{1}}{\sqrt{5}}.

\frac{1}{\sqrt{5}}

Áirigh fréamh chearnach 1 agus faigh 1.

\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{5} chun ainmneoir \frac{1}{\sqrt{5}} a thiontú in uimhir chóimheasta.

\frac{\sqrt{5}}{5}

Is é 5 uimhir chearnach \sqrt{5}.