Whakaoti i te sqrt{75}*frac{sqrt{6}}{3}div1/sqrt{2}

$$\sqrt { 75 } \times \frac { \sqrt { 6 } } { 3 } \div \frac { 1 } { \sqrt { 2 } }$$

Aromātai

$$10$$

Ngā Upane Otinga

Tauwehea te 75=5^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 3} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{3}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{5\sqrt{3}\times \frac{\sqrt{6}}{3}}{\frac{1}{\sqrt{2}}}$$

Tuhia te 5\times \frac{\sqrt{6}}{3} hei hautanga kotahi.

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{1}{\sqrt{2}}}$$

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

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{\sqrt{2}}{2}}$$

Tuhia te \frac{5\sqrt{6}}{3}\sqrt{3} hei hautanga kotahi.

$$\frac{\frac{5\sqrt{6}\sqrt{3}}{3}}{\frac{\sqrt{2}}{2}}$$

Whakawehe \frac{5\sqrt{6}\sqrt{3}}{3} ki te \frac{\sqrt{2}}{2} mā te whakarea \frac{5\sqrt{6}\sqrt{3}}{3} ki te tau huripoki o \frac{\sqrt{2}}{2}.

$$\frac{5\sqrt{6}\sqrt{3}\times 2}{3\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{5\sqrt{6}\sqrt{3}\times 2}{3\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{5\sqrt{6}\sqrt{3}\times 2\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{5\sqrt{6}\sqrt{3}\times 2\sqrt{2}}{3\times 2}$$

Tauwehea te 6=3\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3\times 2} hei hua o ngā pūtake rua \sqrt{3}\sqrt{2}.

$$\frac{5\sqrt{3}\sqrt{2}\sqrt{3}\times 2\sqrt{2}}{3\times 2}$$

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

$$\frac{5\times 3\sqrt{2}\times 2\sqrt{2}}{3\times 2}$$

Whakareatia te 5 ki te 3, ka 15.

$$\frac{15\sqrt{2}\times 2\sqrt{2}}{3\times 2}$$

Whakareatia te 15 ki te 2, ka 30.

$$\frac{30\sqrt{2}\sqrt{2}}{3\times 2}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$\frac{30\times 2}{3\times 2}$$

Whakareatia te 30 ki te 2, ka 60.

$$\frac{60}{3\times 2}$$

Whakareatia te 3 ki te 2, ka 6.

$$\frac{60}{6}$$

Whakawehea te 60 ki te 6, kia riro ko 10.

$$10$$

Tauwehe

$$2\times 5$$