Whakaoti i te 1/5+2/391/9-sqrt{1/3}*sqrt{frac{1}{3}}

$$\frac{ 1 }{ 5 } + \frac{ 2 }{ 3 } 9 \frac{ 1 }{ 9 } - \sqrt{ \frac{ 1 }{ 3 } } \times \sqrt{ \frac{ 1 }{ 3 } }$$

Aromātai

$$\frac{802}{135}\approx 5.940740741$$

Ngā Upane Otinga

Whakareatia te \sqrt{\frac{1}{3}} ki te \sqrt{\frac{1}{3}}, ka \frac{1}{3}.

$$\frac{1}{5}+\frac{2}{3}\times \frac{9\times 9+1}{9}-\frac{1}{3}$$

Whakareatia te 9 ki te 9, ka 81.

$$\frac{1}{5}+\frac{2}{3}\times \frac{81+1}{9}-\frac{1}{3}$$

Tāpirihia te 81 ki te 1, ka 82.

$$\frac{1}{5}+\frac{2}{3}\times \frac{82}{9}-\frac{1}{3}$$

Me whakarea te \frac{2}{3} ki te \frac{82}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1}{5}+\frac{2\times 82}{3\times 9}-\frac{1}{3}$$

Mahia ngā whakarea i roto i te hautanga \frac{2\times 82}{3\times 9}.

$$\frac{1}{5}+\frac{164}{27}-\frac{1}{3}$$

Ko te maha noa iti rawa atu o 5 me 27 ko 135. Me tahuri \frac{1}{5} me \frac{164}{27} ki te hautau me te tautūnga 135.

$$\frac{27}{135}+\frac{820}{135}-\frac{1}{3}$$

Tā te mea he rite te tauraro o \frac{27}{135} me \frac{820}{135}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{27+820}{135}-\frac{1}{3}$$

Tāpirihia te 27 ki te 820, ka 847.

$$\frac{847}{135}-\frac{1}{3}$$

Ko te maha noa iti rawa atu o 135 me 3 ko 135. Me tahuri \frac{847}{135} me \frac{1}{3} ki te hautau me te tautūnga 135.

$$\frac{847}{135}-\frac{45}{135}$$

Tā te mea he rite te tauraro o \frac{847}{135} me \frac{45}{135}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{847-45}{135}$$

Tangohia te 45 i te 847, ka 802.

$$\frac{802}{135}$$

Tauwehe

$$\frac{2 \cdot 401}{3 ^ {3} \cdot 5} = 5\frac{127}{135} = 5.940740740740741$$