Whakaoti i te (3sqrt{48}-4sqrt{2})div2sqrt{3})

$$( 3 \sqrt { 48 } - 4 \sqrt { 2 } ) \div 2 \sqrt { 3 } )$$

Aromātai

$$18-2\sqrt{6}\approx 13.101020514$$

Ngā Upane Otinga

Tauwehea te 48=4^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 3} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{3}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{3\times 4\sqrt{3}-4\sqrt{2}}{2}\sqrt{3}$$

Whakareatia te 3 ki te 4, ka 12.

$$\frac{12\sqrt{3}-4\sqrt{2}}{2}\sqrt{3}$$

Tuhia te \frac{12\sqrt{3}-4\sqrt{2}}{2}\sqrt{3} hei hautanga kotahi.

$$\frac{\left(12\sqrt{3}-4\sqrt{2}\right)\sqrt{3}}{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 12\sqrt{3}-4\sqrt{2} ki te \sqrt{3}.

$$\frac{12\left(\sqrt{3}\right)^{2}-4\sqrt{2}\sqrt{3}}{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{12\times 3-4\sqrt{2}\sqrt{3}}{2}$$

Whakareatia te 12 ki te 3, ka 36.

$$\frac{36-4\sqrt{2}\sqrt{3}}{2}$$

Hei whakarea \sqrt{2} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{36-4\sqrt{6}}{2}$$