Whakaoti i te 2(1/sqrt{2}+sqrt{3})-6(1/sqrt{2}-1/sqrt{3})*6

$$2 ( \frac { 1 } { \sqrt { 2 } } + \sqrt { 3 } ) - 6 ( \frac { 1 } { \sqrt { 2 } } - \frac { 1 } { \sqrt { 3 } } ) \cdot 6$$

Aromātai

$$14\sqrt{3}-17\sqrt{2}\approx 0.207080746$$

Ngā Hipanga Rongoā Poto

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

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

Ko te pūrua o \sqrt{2} ko 2.

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

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

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

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

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

Me whakakore te 2 me te 2.

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

Whakareatia te 6 ki te 6, ka 36.

$$\sqrt{2}+2\sqrt{3}-36\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}\right)$$

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

$$\sqrt{2}+2\sqrt{3}-36\left(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{1}{\sqrt{3}}\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$\sqrt{2}+2\sqrt{3}-36\left(\frac{\sqrt{2}}{2}-\frac{1}{\sqrt{3}}\right)$$

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

$$\sqrt{2}+2\sqrt{3}-36\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)$$

Ko te pūrua o \sqrt{3} ko 3.

$$\sqrt{2}+2\sqrt{3}-36\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{3}\right)$$

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{\sqrt{2}}{2} ki te \frac{3}{3}. Whakareatia \frac{\sqrt{3}}{3} ki te \frac{2}{2}.

$$\sqrt{2}+2\sqrt{3}-36\left(\frac{3\sqrt{2}}{6}-\frac{2\sqrt{3}}{6}\right)$$

Tā te mea he rite te tauraro o \frac{3\sqrt{2}}{6} me \frac{2\sqrt{3}}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{2}+2\sqrt{3}-36\times \frac{3\sqrt{2}-2\sqrt{3}}{6}$$

Whakakorea atu te tauwehe pūnoa nui rawa 6 i roto i te 36 me te 6.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -6 ki te 3\sqrt{2}-2\sqrt{3}.

$$\sqrt{2}+2\sqrt{3}-18\sqrt{2}+12\sqrt{3}$$

Pahekotia te \sqrt{2} me -18\sqrt{2}, ka -17\sqrt{2}.

$$-17\sqrt{2}+2\sqrt{3}+12\sqrt{3}$$

Pahekotia te 2\sqrt{3} me 12\sqrt{3}, ka 14\sqrt{3}.

$$-17\sqrt{2}+14\sqrt{3}$$

Tauwehe

$$14 \sqrt{3} - 17 \sqrt{2} = 0.207080746$$