Whakaoti i te 2sqrt{3}-1/2*sqrt{5}*sqrt{3}divsqrt{20}

$$2 \sqrt { 3 } - \frac { 1 } { 2 } \times \sqrt { 5 } \times \sqrt { 3 } \div \sqrt { 20 }$$

Aromātai

$$\frac{7\sqrt{3}}{4}\approx 3.031088913$$

Ngā Upane Otinga

Hei whakarea \sqrt{5} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}}{\sqrt{20}}$$

Tauwehea te 20=2^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 5} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{5}. Tuhia te pūtakerua o te 2^{2}.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}}{2\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{\frac{1}{2}\sqrt{15}}{2\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}\sqrt{5}}{2\times 5}$$

Tauwehea te 15=5\times 3. Tuhia anō te pūtake rua o te hua \sqrt{5\times 3} hei hua o ngā pūtake rua \sqrt{5}\sqrt{3}.

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

Whakareatia te \sqrt{5} ki te \sqrt{5}, ka 5.

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

Whakareatia te 2 ki te 5, ka 10.

$$2\sqrt{3}-\frac{\frac{1}{2}\times 5\sqrt{3}}{10}$$

Whakareatia te \frac{1}{2} ki te 5, ka \frac{5}{2}.

$$2\sqrt{3}-\frac{\frac{5}{2}\sqrt{3}}{10}$$

Whakawehea te \frac{5}{2}\sqrt{3} ki te 10, kia riro ko \frac{1}{4}\sqrt{3}.

$$2\sqrt{3}-\frac{1}{4}\sqrt{3}$$

Pahekotia te 2\sqrt{3} me -\frac{1}{4}\sqrt{3}, ka \frac{7}{4}\sqrt{3}.

$$\frac{7}{4}\sqrt{3}$$