Réitigh frac{5sqrt{2}+3sqrt{3}}{3sqrt{2}+2sqrt{3}}

$$\frac { 5 \sqrt { 2 } + 3 \sqrt { 3 } } { 3 \sqrt { 2 } + 2 \sqrt { 3 } }$$

Luacháil

$$-\frac{\sqrt{6}}{6}+2\approx 1.59175171$$

Céimeanna Réitigh

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

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

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

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

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

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

Ríomh cumhacht 3 de 2 agus faigh 9.

$$\frac{\left(5\sqrt{2}+3\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{9\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{\left(5\sqrt{2}+3\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{9\times 2-\left(2\sqrt{3}\right)^{2}}$$

Méadaigh 9 agus 2 chun 18 a fháil.

$$\frac{\left(5\sqrt{2}+3\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{18-\left(2\sqrt{3}\right)^{2}}$$

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

$$\frac{\left(5\sqrt{2}+3\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{18-2^{2}\left(\sqrt{3}\right)^{2}}$$

Ríomh cumhacht 2 de 2 agus faigh 4.

$$\frac{\left(5\sqrt{2}+3\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{18-4\left(\sqrt{3}\right)^{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{\left(5\sqrt{2}+3\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{18-4\times 3}$$

Méadaigh 4 agus 3 chun 12 a fháil.

$$\frac{\left(5\sqrt{2}+3\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{18-12}$$

Dealaigh 12 ó 18 chun 6 a fháil.

$$\frac{\left(5\sqrt{2}+3\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{6}$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 5\sqrt{2}+3\sqrt{3} a iolrú faoi gach téarma de 3\sqrt{2}-2\sqrt{3}.

$$\frac{15\left(\sqrt{2}\right)^{2}-10\sqrt{3}\sqrt{2}+9\sqrt{3}\sqrt{2}-6\left(\sqrt{3}\right)^{2}}{6}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{15\times 2-10\sqrt{3}\sqrt{2}+9\sqrt{3}\sqrt{2}-6\left(\sqrt{3}\right)^{2}}{6}$$

Méadaigh 15 agus 2 chun 30 a fháil.

$$\frac{30-10\sqrt{3}\sqrt{2}+9\sqrt{3}\sqrt{2}-6\left(\sqrt{3}\right)^{2}}{6}$$

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

$$\frac{30-10\sqrt{6}+9\sqrt{3}\sqrt{2}-6\left(\sqrt{3}\right)^{2}}{6}$$

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

$$\frac{30-10\sqrt{6}+9\sqrt{6}-6\left(\sqrt{3}\right)^{2}}{6}$$

Comhcheangail -10\sqrt{6} agus 9\sqrt{6} chun -\sqrt{6} a fháil.

$$\frac{30-\sqrt{6}-6\left(\sqrt{3}\right)^{2}}{6}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{30-\sqrt{6}-6\times 3}{6}$$

Méadaigh -6 agus 3 chun -18 a fháil.

$$\frac{30-\sqrt{6}-18}{6}$$

Dealaigh 18 ó 30 chun 12 a fháil.

$$\frac{12-\sqrt{6}}{6}$$