Whakaoti i te sqrt{15/25-36/21+123/50}

$$\sqrt { \frac { 15 } { 25 } - \frac { 36 } { 21 } + \frac { 123 } { 50 } }$$

Aromātai

$$\frac{\sqrt{6594}}{70}\approx 1.16004926$$

Ngā Upane Otinga

Whakahekea te hautanga \frac{15}{25} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\frac{3}{5}-\frac{36}{21}+\frac{123}{50}}$$

Whakahekea te hautanga \frac{36}{21} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{\frac{3}{5}-\frac{12}{7}+\frac{123}{50}}$$

Ko te maha noa iti rawa atu o 5 me 7 ko 35. Me tahuri \frac{3}{5} me \frac{12}{7} ki te hautau me te tautūnga 35.

$$\sqrt{\frac{21}{35}-\frac{60}{35}+\frac{123}{50}}$$

Tā te mea he rite te tauraro o \frac{21}{35} me \frac{60}{35}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{21-60}{35}+\frac{123}{50}}$$

Tangohia te 60 i te 21, ka -39.

$$\sqrt{-\frac{39}{35}+\frac{123}{50}}$$

Ko te maha noa iti rawa atu o 35 me 50 ko 350. Me tahuri -\frac{39}{35} me \frac{123}{50} ki te hautau me te tautūnga 350.

$$\sqrt{-\frac{390}{350}+\frac{861}{350}}$$

Tā te mea he rite te tauraro o -\frac{390}{350} me \frac{861}{350}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{-390+861}{350}}$$

Tāpirihia te -390 ki te 861, ka 471.

$$\sqrt{\frac{471}{350}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{471}{350}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{471}}{\sqrt{350}}.

$$\frac{\sqrt{471}}{\sqrt{350}}$$

Tauwehea te 350=5^{2}\times 14. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 14} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{14}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{\sqrt{471}}{5\sqrt{14}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{471}}{5\sqrt{14}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{14}.

$$\frac{\sqrt{471}\sqrt{14}}{5\left(\sqrt{14}\right)^{2}}$$

Ko te pūrua o \sqrt{14} ko 14.

$$\frac{\sqrt{471}\sqrt{14}}{5\times 14}$$

Hei whakarea \sqrt{471} me \sqrt{14}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{6594}}{5\times 14}$$

Whakareatia te 5 ki te 14, ka 70.

$$\frac{\sqrt{6594}}{70}$$