Whakaoti i te sqrt{78*45/12}

$$\sqrt{ 78 \times \frac{ 45 }{ 12 } }$$

Aromātai

$$\frac{3\sqrt{130}}{2}\approx 17.102631376$$

Ngā Upane Otinga

Whakahekea te hautanga \frac{45}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{78\times \frac{15}{4}}$$

Tuhia te 78\times \frac{15}{4} hei hautanga kotahi.

$$\sqrt{\frac{78\times 15}{4}}$$

Whakareatia te 78 ki te 15, ka 1170.

$$\sqrt{\frac{1170}{4}}$$

Whakahekea te hautanga \frac{1170}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{\frac{585}{2}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{585}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{585}}{\sqrt{2}}.

$$\frac{\sqrt{585}}{\sqrt{2}}$$

Tauwehea te 585=3^{2}\times 65. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 65} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{65}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{3\sqrt{65}}{\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{3\sqrt{65}}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{3\sqrt{65}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{3\sqrt{65}\sqrt{2}}{2}$$

Hei whakarea \sqrt{65} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{3\sqrt{130}}{2}$$