Réitigh frac{3sqrt{3}-2}{2sqrt{7}+1}

$$\frac { 3 \sqrt { 3 } - 2 } { 2 \sqrt { 7 } + 1 }$$

Luacháil

$$\frac{2\sqrt{21}}{9}-\frac{\sqrt{3}}{9}-\frac{4\sqrt{7}}{27}+\frac{2}{27}\approx 0.508010982$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 2\sqrt{7}-1 chun ainmneoir \frac{3\sqrt{3}-2}{2\sqrt{7}+1} a thiontú in uimhir chóimheasta.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{\left(2\sqrt{7}+1\right)\left(2\sqrt{7}-1\right)}$$

Mar shampla \left(2\sqrt{7}+1\right)\left(2\sqrt{7}-1\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}.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{\left(2\sqrt{7}\right)^{2}-1^{2}}$$

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

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{2^{2}\left(\sqrt{7}\right)^{2}-1^{2}}$$

Ríomh cumhacht 2 de 2 agus faigh 4.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{4\left(\sqrt{7}\right)^{2}-1^{2}}$$

Is é 7 uimhir chearnach \sqrt{7}.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{4\times 7-1^{2}}$$

Méadaigh 4 agus 7 chun 28 a fháil.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{28-1^{2}}$$

Ríomh cumhacht 1 de 2 agus faigh 1.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{28-1}$$

Dealaigh 1 ó 28 chun 27 a fháil.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{27}$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 3\sqrt{3}-2 a iolrú faoi gach téarma de 2\sqrt{7}-1.

$$\frac{6\sqrt{3}\sqrt{7}-3\sqrt{3}-4\sqrt{7}+2}{27}$$

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

$$\frac{6\sqrt{21}-3\sqrt{3}-4\sqrt{7}+2}{27}$$