Réitigh frac{2+sqrt{3}}{3sqrt{2}+2sqrt{7}}

$$\frac { 2 + \sqrt { 3 } } { 3 \sqrt { 2 } + 2 \sqrt { 7 } }$$

Luacháil

$$\frac{\sqrt{21}}{5}+\frac{2\sqrt{7}}{5}-\frac{3\sqrt{2}}{5}-\frac{3\sqrt{6}}{10}\approx 0.391440603$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 3\sqrt{2}-2\sqrt{7} chun ainmneoir \frac{2+\sqrt{3}}{3\sqrt{2}+2\sqrt{7}} a thiontú in uimhir chóimheasta.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{\left(3\sqrt{2}+2\sqrt{7}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}$$

Mar shampla \left(3\sqrt{2}+2\sqrt{7}\right)\left(3\sqrt{2}-2\sqrt{7}\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}.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{7}\right)^{2}}$$

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

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{3^{2}\left(\sqrt{2}\right)^{2}-\left(2\sqrt{7}\right)^{2}}$$

Ríomh cumhacht 3 de 2 agus faigh 9.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{9\left(\sqrt{2}\right)^{2}-\left(2\sqrt{7}\right)^{2}}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{9\times 2-\left(2\sqrt{7}\right)^{2}}$$

Méadaigh 9 agus 2 chun 18 a fháil.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-\left(2\sqrt{7}\right)^{2}}$$

Fairsingigh \left(2\sqrt{7}\right)^{2}

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-2^{2}\left(\sqrt{7}\right)^{2}}$$

Ríomh cumhacht 2 de 2 agus faigh 4.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-4\left(\sqrt{7}\right)^{2}}$$

Is é 7 uimhir chearnach \sqrt{7}.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-4\times 7}$$

Méadaigh 4 agus 7 chun 28 a fháil.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-28}$$

Dealaigh 28 ó 18 chun -10 a fháil.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{-10}$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 2+\sqrt{3} a iolrú faoi gach téarma de 3\sqrt{2}-2\sqrt{7}.

$$\frac{6\sqrt{2}-4\sqrt{7}+3\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{7}}{-10}$$

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

$$\frac{6\sqrt{2}-4\sqrt{7}+3\sqrt{6}-2\sqrt{3}\sqrt{7}}{-10}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{3} agus \sqrt{7} a iolrú.

$$\frac{6\sqrt{2}-4\sqrt{7}+3\sqrt{6}-2\sqrt{21}}{-10}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi -1.

$$\frac{-6\sqrt{2}+4\sqrt{7}-3\sqrt{6}+2\sqrt{21}}{10}$$