Whakaoti i te sqrt{15}div(sqrt{5}+sqrt{3})

$$\sqrt{ 15 } \div ( \sqrt{ 5 } + \sqrt{ 3 } )$$

Aromātai

$$\frac{\sqrt{5}\left(\sqrt{15}-3\right)}{2}\approx 0.976025053$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{\sqrt{15}}{\sqrt{5}+\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}-\sqrt{3}.

$$\frac{\sqrt{15}\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}$$

Whakaarohia te \left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Pūrua \sqrt{5}. Pūrua \sqrt{3}.

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

Tangohia te 3 i te 5, ka 2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{15} ki te \sqrt{5}-\sqrt{3}.

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

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}.

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

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

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

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

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

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

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