Réitigh 1/2sqrt{48}div(3sqrt{2}-sqrt{3})

$$\frac { 1 } { 2 } \sqrt { 48 } \div ( 3 \sqrt { 2 } - \sqrt { 3 } )$$

Luacháil

$$\frac{2\left(\sqrt{6}+1\right)}{5}\approx 1.379795897$$

Céimeanna Réitigh

Fachtóirigh 48=4^{2}\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{4^{2}\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{4^{2}}\sqrt{3}. Tóg fréamh chearnach 4^{2}.

$$\frac{\frac{1}{2}\times 4\sqrt{3}}{3\sqrt{2}-\sqrt{3}}$$

Méadaigh \frac{1}{2} agus 4 chun \frac{4}{2} a fháil.

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

Roinn 4 faoi 2 chun 2 a fháil.

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

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

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

Mar shampla \left(3\sqrt{2}-\sqrt{3}\right)\left(3\sqrt{2}+\sqrt{3}\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}.

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

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

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

Ríomh cumhacht 3 de 2 agus faigh 9.

$$\frac{2\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)}{9\left(\sqrt{2}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{2\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)}{9\times 2-\left(\sqrt{3}\right)^{2}}$$

Méadaigh 9 agus 2 chun 18 a fháil.

$$\frac{2\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)}{18-\left(\sqrt{3}\right)^{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{2\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)}{18-3}$$

Dealaigh 3 ó 18 chun 15 a fháil.

$$\frac{2\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)}{15}$$

Úsáid an t-airí dáileach chun 2\sqrt{3} a mhéadú faoi 3\sqrt{2}+\sqrt{3}.

$$\frac{6\sqrt{3}\sqrt{2}+2\left(\sqrt{3}\right)^{2}}{15}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{3} agus \sqrt{2} a iolrú.

$$\frac{6\sqrt{6}+2\left(\sqrt{3}\right)^{2}}{15}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{6\sqrt{6}+2\times 3}{15}$$

Méadaigh 2 agus 3 chun 6 a fháil.

$$\frac{6\sqrt{6}+6}{15}$$