Réitigh 1/sqrt{27+sqrt{12}+5sqrt{2}}-4/5sqrt{2}

$$\frac { 1 } { \sqrt { 27 } + \sqrt { 12 } + 5 \sqrt { 2 } } - \frac { 4 } { 5 \sqrt { 2 } }$$

Luacháil

$$\frac{\sqrt{3}-3\sqrt{2}}{5}\approx -0.502117976$$

Céimeanna gearra réitigh

Fachtóirigh 27=3^{2}\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{3^{2}\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{3^{2}}\sqrt{3}. Tóg fréamh chearnach 3^{2}.

$$\frac{1}{3\sqrt{3}+\sqrt{12}+5\sqrt{2}}-\frac{4}{5\sqrt{2}}$$

Fachtóirigh 12=2^{2}\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{3}. Tóg fréamh chearnach 2^{2}.

$$\frac{1}{3\sqrt{3}+2\sqrt{3}+5\sqrt{2}}-\frac{4}{5\sqrt{2}}$$

Comhcheangail 3\sqrt{3} agus 2\sqrt{3} chun 5\sqrt{3} a fháil.

$$\frac{1}{5\sqrt{3}+5\sqrt{2}}-\frac{4}{5\sqrt{2}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 5\sqrt{3}-5\sqrt{2} chun ainmneoir \frac{1}{5\sqrt{3}+5\sqrt{2}} a thiontú in uimhir chóimheasta.

$$\frac{5\sqrt{3}-5\sqrt{2}}{\left(5\sqrt{3}+5\sqrt{2}\right)\left(5\sqrt{3}-5\sqrt{2}\right)}-\frac{4}{5\sqrt{2}}$$

Mar shampla \left(5\sqrt{3}+5\sqrt{2}\right)\left(5\sqrt{3}-5\sqrt{2}\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{5\sqrt{3}-5\sqrt{2}}{\left(5\sqrt{3}\right)^{2}-\left(5\sqrt{2}\right)^{2}}-\frac{4}{5\sqrt{2}}$$

Fairsingigh \left(5\sqrt{3}\right)^{2}

$$\frac{5\sqrt{3}-5\sqrt{2}}{5^{2}\left(\sqrt{3}\right)^{2}-\left(5\sqrt{2}\right)^{2}}-\frac{4}{5\sqrt{2}}$$

Ríomh cumhacht 5 de 2 agus faigh 25.

$$\frac{5\sqrt{3}-5\sqrt{2}}{25\left(\sqrt{3}\right)^{2}-\left(5\sqrt{2}\right)^{2}}-\frac{4}{5\sqrt{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{5\sqrt{3}-5\sqrt{2}}{25\times 3-\left(5\sqrt{2}\right)^{2}}-\frac{4}{5\sqrt{2}}$$

Méadaigh 25 agus 3 chun 75 a fháil.

$$\frac{5\sqrt{3}-5\sqrt{2}}{75-\left(5\sqrt{2}\right)^{2}}-\frac{4}{5\sqrt{2}}$$

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

$$\frac{5\sqrt{3}-5\sqrt{2}}{75-5^{2}\left(\sqrt{2}\right)^{2}}-\frac{4}{5\sqrt{2}}$$

Ríomh cumhacht 5 de 2 agus faigh 25.

$$\frac{5\sqrt{3}-5\sqrt{2}}{75-25\left(\sqrt{2}\right)^{2}}-\frac{4}{5\sqrt{2}}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{5\sqrt{3}-5\sqrt{2}}{75-25\times 2}-\frac{4}{5\sqrt{2}}$$

Méadaigh 25 agus 2 chun 50 a fháil.

$$\frac{5\sqrt{3}-5\sqrt{2}}{75-50}-\frac{4}{5\sqrt{2}}$$

Dealaigh 50 ó 75 chun 25 a fháil.

$$\frac{5\sqrt{3}-5\sqrt{2}}{25}-\frac{4}{5\sqrt{2}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{4}{5\sqrt{2}} a thiontú in uimhir chóimheasta.

$$\frac{5\sqrt{3}-5\sqrt{2}}{25}-\frac{4\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{5\sqrt{3}-5\sqrt{2}}{25}-\frac{4\sqrt{2}}{5\times 2}$$

Cealaigh 2 mar uimhreoir agus ainmneoir.

$$\frac{5\sqrt{3}-5\sqrt{2}}{25}-\frac{2\sqrt{2}}{5}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de 25 agus 5 ná 25. Méadaigh \frac{2\sqrt{2}}{5} faoi \frac{5}{5}.

$$\frac{5\sqrt{3}-5\sqrt{2}}{25}-\frac{5\times 2\sqrt{2}}{25}$$

Tá an t-ainmneoir céanna ag \frac{5\sqrt{3}-5\sqrt{2}}{25} agus \frac{5\times 2\sqrt{2}}{25} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{5\sqrt{3}-5\sqrt{2}-5\times 2\sqrt{2}}{25}$$

Déan iolrúcháin in 5\sqrt{3}-5\sqrt{2}-5\times 2\sqrt{2}.

$$\frac{5\sqrt{3}-5\sqrt{2}-10\sqrt{2}}{25}$$

Déan áirimh in 5\sqrt{3}-5\sqrt{2}-10\sqrt{2}.

$$\frac{5\sqrt{3}-15\sqrt{2}}{25}$$

Fachtóirigh

$$\frac{\sqrt{3} - 3 \sqrt{2}}{5} = -0.5021179759100817$$