Whakaoti i te frac{4sqrt{5}}{2sqrt{3}+sqrt{14}}

$$\frac { 4 \sqrt { 5 } } { 2 \sqrt { 3 } + \sqrt { 14 } }$$

Aromātai

$$2\sqrt{70}-4\sqrt{15}\approx 1.241267146$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{4\sqrt{5}}{2\sqrt{3}+\sqrt{14}} mā te whakarea i te taurunga me te tauraro ki te 2\sqrt{3}-\sqrt{14}.

$$\frac{4\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right)}{\left(2\sqrt{3}+\sqrt{14}\right)\left(2\sqrt{3}-\sqrt{14}\right)}$$

Whakaarohia te \left(2\sqrt{3}+\sqrt{14}\right)\left(2\sqrt{3}-\sqrt{14}\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}.

$$\frac{4\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right)}{\left(2\sqrt{3}\right)^{2}-\left(\sqrt{14}\right)^{2}}$$

Whakarohaina te \left(2\sqrt{3}\right)^{2}.

$$\frac{4\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right)}{2^{2}\left(\sqrt{3}\right)^{2}-\left(\sqrt{14}\right)^{2}}$$

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

$$\frac{4\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right)}{4\left(\sqrt{3}\right)^{2}-\left(\sqrt{14}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{4\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right)}{4\times 3-\left(\sqrt{14}\right)^{2}}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{4\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right)}{12-\left(\sqrt{14}\right)^{2}}$$

Ko te pūrua o \sqrt{14} ko 14.

$$\frac{4\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right)}{12-14}$$

Tangohia te 14 i te 12, ka -2.

$$\frac{4\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right)}{-2}$$

Whakawehea te 4\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right) ki te -2, kia riro ko -2\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right).

$$-2\sqrt{5}\left(2\sqrt{3}-\sqrt{14}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2\sqrt{5} ki te 2\sqrt{3}-\sqrt{14}.

$$-4\sqrt{3}\sqrt{5}+2\sqrt{5}\sqrt{14}$$

Hei whakarea \sqrt{3} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$-4\sqrt{15}+2\sqrt{5}\sqrt{14}$$

Hei whakarea \sqrt{5} me \sqrt{14}, whakareatia ngā tau i raro i te pūtake rua.

$$-4\sqrt{15}+2\sqrt{70}$$