Whakaoti i te frac{2sqrt{5}+4sqrt{3}}{sqrt{2}}-frac{2sqrt{18}-sqrt{27}}{sqrt{3}}

$$\frac { 2 \sqrt { 5 } + 4 \sqrt { 3 } } { \sqrt { 2 } } - \frac { 2 \sqrt { 18 } - \sqrt { 27 } } { \sqrt { 3 } }$$

Aromātai

$$\sqrt{10}+3\approx 6.16227766$$

Ngā Hipanga Rongoā Poto

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

$$\frac{\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{2\sqrt{18}-\sqrt{27}}{\sqrt{3}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{2}-\frac{2\sqrt{18}-\sqrt{27}}{\sqrt{3}}$$

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}.

$$\frac{\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{2}-\frac{2\times 3\sqrt{2}-\sqrt{27}}{\sqrt{3}}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{2}-\frac{6\sqrt{2}-\sqrt{27}}{\sqrt{3}}$$

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{2}-\frac{6\sqrt{2}-3\sqrt{3}}{\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{6\sqrt{2}-3\sqrt{3}}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{2}-\frac{\left(6\sqrt{2}-3\sqrt{3}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{2}-\frac{\left(6\sqrt{2}-3\sqrt{3}\right)\sqrt{3}}{3}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2 me 3 ko 6. Whakareatia \frac{\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{2} ki te \frac{3}{3}. Whakareatia \frac{\left(6\sqrt{2}-3\sqrt{3}\right)\sqrt{3}}{3} ki te \frac{2}{2}.

$$\frac{3\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{6}-\frac{2\left(6\sqrt{2}-3\sqrt{3}\right)\sqrt{3}}{6}$$

Tā te mea he rite te tauraro o \frac{3\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}}{6} me \frac{2\left(6\sqrt{2}-3\sqrt{3}\right)\sqrt{3}}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}-2\left(6\sqrt{2}-3\sqrt{3}\right)\sqrt{3}}{6}$$

Mahia ngā whakarea i roto o 3\left(2\sqrt{5}+4\sqrt{3}\right)\sqrt{2}-2\left(6\sqrt{2}-3\sqrt{3}\right)\sqrt{3}.

$$\frac{6\sqrt{10}+12\sqrt{6}-12\sqrt{6}+18}{6}$$

Mahia ngā tātaitai i roto o 6\sqrt{10}+12\sqrt{6}-12\sqrt{6}+18.

$$\frac{6\sqrt{10}+18}{6}$$

Whakawehea ia wā o 6\sqrt{10}+18 ki te 6, kia riro ko \sqrt{10}+3.

$$\sqrt{10}+3$$