Whakaoti i te sqrt{45}divsqrt{32}*sqrt{8}

$$\sqrt { 45 } \div \sqrt { 32 } \cdot \sqrt { 8 }$$

Aromātai

$$\frac{3\sqrt{5}}{2}\approx 3.354101966$$

Ngā Upane Otinga

Tauwehea te 45=3^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 5} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{5}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{3\sqrt{5}}{\sqrt{32}}\sqrt{8}$$

Tauwehea te 32=4^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 2} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{2}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{3\sqrt{5}}{4\sqrt{2}}\sqrt{8}$$

Whakangāwaritia te tauraro o \frac{3\sqrt{5}}{4\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{3\sqrt{5}\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}\sqrt{8}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{3\sqrt{5}\sqrt{2}}{4\times 2}\sqrt{8}$$

Hei whakarea \sqrt{5} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{3\sqrt{10}}{4\times 2}\sqrt{8}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{3\sqrt{10}}{8}\sqrt{8}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{3\sqrt{10}}{8}\times 2\sqrt{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 8 i roto i te 2 me te 8.

$$\frac{3\sqrt{10}}{4}\sqrt{2}$$

Tuhia te \frac{3\sqrt{10}}{4}\sqrt{2} hei hautanga kotahi.

$$\frac{3\sqrt{10}\sqrt{2}}{4}$$

Tauwehea te 10=2\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2\times 5} hei hua o ngā pūtake rua \sqrt{2}\sqrt{5}.

$$\frac{3\sqrt{2}\sqrt{5}\sqrt{2}}{4}$$

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

$$\frac{3\times 2\sqrt{5}}{4}$$

Whakareatia te 3 ki te 2, ka 6.

$$\frac{6\sqrt{5}}{4}$$

Whakawehea te 6\sqrt{5} ki te 4, kia riro ko \frac{3}{2}\sqrt{5}.

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