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

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

Luacháil

$$\frac{\sqrt{21}-5}{2}\approx -0.208712153$$

Céimeanna Réitigh

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

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

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

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

Cearnóg \sqrt{3}. Cearnóg \sqrt{7}.

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

Dealaigh 7 ó 3 chun -4 a fháil.

$$\frac{\left(\sqrt{3}-\sqrt{7}\right)\left(\sqrt{3}-\sqrt{7}\right)}{-4}$$

Méadaigh \sqrt{3}-\sqrt{7} agus \sqrt{3}-\sqrt{7} chun \left(\sqrt{3}-\sqrt{7}\right)^{2} a fháil.

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

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(\sqrt{3}-\sqrt{7}\right)^{2} a leathnú.

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

Is é 3 uimhir chearnach \sqrt{3}.

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

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

$$\frac{3-2\sqrt{21}+\left(\sqrt{7}\right)^{2}}{-4}$$

Is é 7 uimhir chearnach \sqrt{7}.

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

Suimigh 3 agus 7 chun 10 a fháil.

$$\frac{10-2\sqrt{21}}{-4}$$