Whakaoti i te sqrt{6}div(1/sqrt{3}+sqrt{2})+sqrt{50}

$$\sqrt { 6 } \div ( \frac { 1 } { \sqrt { 3 } } + \sqrt { 2 } ) + \sqrt { 50 }$$

Aromātai

$$\frac{2\left(3\sqrt{3}+11\sqrt{2}\right)}{5}\approx 8.301000644$$

Ngā Hipanga Rongoā Poto

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

$$\frac{\sqrt{6}}{\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{2}}+\sqrt{50}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\sqrt{6}}{\frac{\sqrt{3}}{3}+\sqrt{2}}+\sqrt{50}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia \sqrt{2} ki te \frac{3}{3}.

$$\frac{\sqrt{6}}{\frac{\sqrt{3}}{3}+\frac{3\sqrt{2}}{3}}+\sqrt{50}$$

Tā te mea he rite te tauraro o \frac{\sqrt{3}}{3} me \frac{3\sqrt{2}}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\sqrt{6}}{\frac{\sqrt{3}+3\sqrt{2}}{3}}+\sqrt{50}$$

Whakawehe \sqrt{6} ki te \frac{\sqrt{3}+3\sqrt{2}}{3} mā te whakarea \sqrt{6} ki te tau huripoki o \frac{\sqrt{3}+3\sqrt{2}}{3}.

$$\frac{\sqrt{6}\times 3}{\sqrt{3}+3\sqrt{2}}+\sqrt{50}$$

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

$$\frac{\sqrt{6}\times 3\left(\sqrt{3}-3\sqrt{2}\right)}{\left(\sqrt{3}+3\sqrt{2}\right)\left(\sqrt{3}-3\sqrt{2}\right)}+\sqrt{50}$$

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

$$\frac{\sqrt{6}\times 3\left(\sqrt{3}-3\sqrt{2}\right)}{\left(\sqrt{3}\right)^{2}-\left(3\sqrt{2}\right)^{2}}+\sqrt{50}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\sqrt{6}\times 3\left(\sqrt{3}-3\sqrt{2}\right)}{3-\left(3\sqrt{2}\right)^{2}}+\sqrt{50}$$

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

$$\frac{\sqrt{6}\times 3\left(\sqrt{3}-3\sqrt{2}\right)}{3-3^{2}\left(\sqrt{2}\right)^{2}}+\sqrt{50}$$

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

$$\frac{\sqrt{6}\times 3\left(\sqrt{3}-3\sqrt{2}\right)}{3-9\left(\sqrt{2}\right)^{2}}+\sqrt{50}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\sqrt{6}\times 3\left(\sqrt{3}-3\sqrt{2}\right)}{3-9\times 2}+\sqrt{50}$$

Whakareatia te 9 ki te 2, ka 18.

$$\frac{\sqrt{6}\times 3\left(\sqrt{3}-3\sqrt{2}\right)}{3-18}+\sqrt{50}$$

Tangohia te 18 i te 3, ka -15.

$$\frac{\sqrt{6}\times 3\left(\sqrt{3}-3\sqrt{2}\right)}{-15}+\sqrt{50}$$

Whakawehea te \sqrt{6}\times 3\left(\sqrt{3}-3\sqrt{2}\right) ki te -15, kia riro ko \sqrt{6}\left(-\frac{1}{5}\right)\left(\sqrt{3}-3\sqrt{2}\right).

$$\sqrt{6}\left(-\frac{1}{5}\right)\left(\sqrt{3}-3\sqrt{2}\right)+\sqrt{50}$$

Tauwehea te 50=5^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 2} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{2}. Tuhia te pūtakerua o te 5^{2}.

$$\sqrt{6}\left(-\frac{1}{5}\right)\left(\sqrt{3}-3\sqrt{2}\right)+5\sqrt{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{6}\left(-\frac{1}{5}\right) ki te \sqrt{3}-3\sqrt{2}.

$$\sqrt{6}\left(-\frac{1}{5}\right)\sqrt{3}+\sqrt{6}\left(-\frac{1}{5}\right)\left(-3\right)\sqrt{2}+5\sqrt{2}$$

Tauwehea te 6=3\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3\times 2} hei hua o ngā pūtake rua \sqrt{3}\sqrt{2}.

$$\sqrt{3}\sqrt{2}\left(-\frac{1}{5}\right)\sqrt{3}+\sqrt{6}\left(-\frac{1}{5}\right)\left(-3\right)\sqrt{2}+5\sqrt{2}$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$3\left(-\frac{1}{5}\right)\sqrt{2}+\sqrt{6}\left(-\frac{1}{5}\right)\left(-3\right)\sqrt{2}+5\sqrt{2}$$

Tuhia te 3\left(-\frac{1}{5}\right) hei hautanga kotahi.

$$\frac{3\left(-1\right)}{5}\sqrt{2}+\sqrt{6}\left(-\frac{1}{5}\right)\left(-3\right)\sqrt{2}+5\sqrt{2}$$

Whakareatia te 3 ki te -1, ka -3.

$$\frac{-3}{5}\sqrt{2}+\sqrt{6}\left(-\frac{1}{5}\right)\left(-3\right)\sqrt{2}+5\sqrt{2}$$

Ka taea te hautanga \frac{-3}{5} te tuhi anō ko -\frac{3}{5} mā te tango i te tohu tōraro.

$$-\frac{3}{5}\sqrt{2}+\sqrt{6}\left(-\frac{1}{5}\right)\left(-3\right)\sqrt{2}+5\sqrt{2}$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

$$-\frac{3}{5}\sqrt{2}+\sqrt{2}\sqrt{3}\left(-\frac{1}{5}\right)\left(-3\right)\sqrt{2}+5\sqrt{2}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$-\frac{3}{5}\sqrt{2}+2\left(-\frac{1}{5}\right)\left(-3\right)\sqrt{3}+5\sqrt{2}$$

Tuhia te 2\left(-\frac{1}{5}\right) hei hautanga kotahi.

$$-\frac{3}{5}\sqrt{2}+\frac{2\left(-1\right)}{5}\left(-3\right)\sqrt{3}+5\sqrt{2}$$

Whakareatia te 2 ki te -1, ka -2.

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

Ka taea te hautanga \frac{-2}{5} te tuhi anō ko -\frac{2}{5} mā te tango i te tohu tōraro.

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

Tuhia te -\frac{2}{5}\left(-3\right) hei hautanga kotahi.

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

Whakareatia te -2 ki te -3, ka 6.

$$-\frac{3}{5}\sqrt{2}+\frac{6}{5}\sqrt{3}+5\sqrt{2}$$

Pahekotia te -\frac{3}{5}\sqrt{2} me 5\sqrt{2}, ka \frac{22}{5}\sqrt{2}.

$$\frac{22}{5}\sqrt{2}+\frac{6}{5}\sqrt{3}$$