Whakaoti i te frac{3sqrt{3}-2}{2sqrt{7}+1}

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

Aromātai

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

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{3\sqrt{3}-2}{2\sqrt{7}+1} mā te whakarea i te taurunga me te tauraro ki te 2\sqrt{7}-1.

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

Whakaarohia te \left(2\sqrt{7}+1\right)\left(2\sqrt{7}-1\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Whakarohaina te \left(2\sqrt{7}\right)^{2}.

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Ko te pūrua o \sqrt{7} ko 7.

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

Whakareatia te 4 ki te 7, ka 28.

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

Tātaihia te 1 mā te pū o 2, kia riro ko 1.

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

Tangohia te 1 i te 28, ka 27.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 3\sqrt{3}-2 ki ia tau o 2\sqrt{7}-1.

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

Hei whakarea \sqrt{3} me \sqrt{7}, whakareatia ngā tau i raro i te pūtake rua.

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