Réitigh 60sqrt{1/6}-2sqrt{54}-12sqrt{1/24}

Luacháil

Céimeanna Réitigh

Tráth na gCeist

Arithmetic

5 fadhbanna cosúil le:

Fadhbanna den chineál céanna ó Chuardach Gréasáin

https://socratic.org/questions/how-do-you-simplify-3sqrt-18-sqrt-48-2sqrt-6-sqrt-80

https://math.stackexchange.com/questions/2488268/rationalize-denominator-frac9-sqrt21-sqrt2-2-sqrt5-sqrt10

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

https://www.quora.com/Are-there-any-properties-of-a-square-root-of-the-quotient-of-a-complex-number-Is-sqrt-frac-1-i-1+i-sqrt-frac-1-i-sqrt-1+i

https://socratic.org/questions/how-do-you-order-the-following-from-least-to-greatest-without-a-calculator-5-sqr

https://socratic.org/questions/how-do-you-order-the-following-from-least-to-greatest-7-2-sqrt11-sqrt16-3-3-sqrt

Roinn

Cóipeáladh go dtí an ghearrthaisce

60\times \frac{\sqrt{1}}{\sqrt{6}}-2\sqrt{54}-12\sqrt{\frac{1}{24}}

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{1}{6}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{1}}{\sqrt{6}}.

60\times \frac{1}{\sqrt{6}}-2\sqrt{54}-12\sqrt{\frac{1}{24}}

Áirigh fréamh chearnach 1 agus faigh 1.

60\times \frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}-2\sqrt{54}-12\sqrt{\frac{1}{24}}

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{6} chun ainmneoir \frac{1}{\sqrt{6}} a thiontú in uimhir chóimheasta.

60\times \frac{\sqrt{6}}{6}-2\sqrt{54}-12\sqrt{\frac{1}{24}}

Is é 6 uimhir chearnach \sqrt{6}.

10\sqrt{6}-2\sqrt{54}-12\sqrt{\frac{1}{24}}

Cealaigh an comhfhachtóir 6 is mó in 60 agus 6.

10\sqrt{6}-2\times 3\sqrt{6}-12\sqrt{\frac{1}{24}}

Fachtóirigh 54=3^{2}\times 6. Athscríobh fréamh cearnach an toraidh \sqrt{3^{2}\times 6} mar thoradh na bhfréamhacha cearnacha \sqrt{3^{2}}\sqrt{6}. Tóg fréamh chearnach 3^{2}.

10\sqrt{6}-6\sqrt{6}-12\sqrt{\frac{1}{24}}

Méadaigh -2 agus 3 chun -6 a fháil.

4\sqrt{6}-12\sqrt{\frac{1}{24}}

Comhcheangail 10\sqrt{6} agus -6\sqrt{6} chun 4\sqrt{6} a fháil.

4\sqrt{6}-12\times \frac{\sqrt{1}}{\sqrt{24}}

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{1}{24}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{1}}{\sqrt{24}}.

4\sqrt{6}-12\times \frac{1}{\sqrt{24}}

Áirigh fréamh chearnach 1 agus faigh 1.

4\sqrt{6}-12\times \frac{1}{2\sqrt{6}}

Fachtóirigh 24=2^{2}\times 6. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 6} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{6}. Tóg fréamh chearnach 2^{2}.

4\sqrt{6}-12\times \frac{\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{6} chun ainmneoir \frac{1}{2\sqrt{6}} a thiontú in uimhir chóimheasta.

4\sqrt{6}-12\times \frac{\sqrt{6}}{2\times 6}

Is é 6 uimhir chearnach \sqrt{6}.

4\sqrt{6}-12\times \frac{\sqrt{6}}{12}

Méadaigh 2 agus 6 chun 12 a fháil.

4\sqrt{6}-\sqrt{6}

Cealaigh 12 agus 12.

3\sqrt{6}

Comhcheangail 4\sqrt{6} agus -\sqrt{6} chun 3\sqrt{6} a fháil.