Whakaoti i te =frac{7sqrt{3}-5sqrt{2}}{sqrt{48}+sqrt{18}}

$$= \frac { 7 \sqrt { 3 } - 5 \sqrt { 2 } } { \sqrt { 48 } + \sqrt { 18 } }$$

Aromātai

$$-\frac{41\sqrt{6}}{30}+\frac{19}{5}\approx 0.452364018$$

Ngā Upane Otinga

Tauwehea te 48=4^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 3} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{3}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{7\sqrt{3}-5\sqrt{2}}{4\sqrt{3}+\sqrt{18}}$$

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{7\sqrt{3}-5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{7\sqrt{3}-5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te 4\sqrt{3}-3\sqrt{2}.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{\left(4\sqrt{3}+3\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}$$

Whakaarohia te \left(4\sqrt{3}+3\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\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}.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{\left(4\sqrt{3}\right)^{2}-\left(3\sqrt{2}\right)^{2}}$$

Whakarohaina te \left(4\sqrt{3}\right)^{2}.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{4^{2}\left(\sqrt{3}\right)^{2}-\left(3\sqrt{2}\right)^{2}}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{16\left(\sqrt{3}\right)^{2}-\left(3\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{16\times 3-\left(3\sqrt{2}\right)^{2}}$$

Whakareatia te 16 ki te 3, ka 48.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-\left(3\sqrt{2}\right)^{2}}$$

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

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-3^{2}\left(\sqrt{2}\right)^{2}}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-9\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-9\times 2}$$

Whakareatia te 9 ki te 2, ka 18.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-18}$$

Tangohia te 18 i te 48, ka 30.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{30}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 7\sqrt{3}-5\sqrt{2} ki ia tau o 4\sqrt{3}-3\sqrt{2}.

$$\frac{28\left(\sqrt{3}\right)^{2}-21\sqrt{3}\sqrt{2}-20\sqrt{3}\sqrt{2}+15\left(\sqrt{2}\right)^{2}}{30}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{28\times 3-21\sqrt{3}\sqrt{2}-20\sqrt{3}\sqrt{2}+15\left(\sqrt{2}\right)^{2}}{30}$$

Whakareatia te 28 ki te 3, ka 84.

$$\frac{84-21\sqrt{3}\sqrt{2}-20\sqrt{3}\sqrt{2}+15\left(\sqrt{2}\right)^{2}}{30}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{84-21\sqrt{6}-20\sqrt{3}\sqrt{2}+15\left(\sqrt{2}\right)^{2}}{30}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{84-21\sqrt{6}-20\sqrt{6}+15\left(\sqrt{2}\right)^{2}}{30}$$

Pahekotia te -21\sqrt{6} me -20\sqrt{6}, ka -41\sqrt{6}.

$$\frac{84-41\sqrt{6}+15\left(\sqrt{2}\right)^{2}}{30}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{84-41\sqrt{6}+15\times 2}{30}$$

Whakareatia te 15 ki te 2, ka 30.

$$\frac{84-41\sqrt{6}+30}{30}$$

Tāpirihia te 84 ki te 30, ka 114.

$$\frac{114-41\sqrt{6}}{30}$$