Whakaoti i te frac{21sqrt{15}}{512+5sqrt{3}}

$$\frac { 21 \sqrt { 15 } } { 512 + 5 \sqrt { 3 } }$$

Aromātai

$$\frac{10752\sqrt{15}-315\sqrt{5}}{262069}\approx 0.156210599$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{21\sqrt{15}}{512+5\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 512-5\sqrt{3}.

$$\frac{21\sqrt{15}\left(512-5\sqrt{3}\right)}{\left(512+5\sqrt{3}\right)\left(512-5\sqrt{3}\right)}$$

Whakaarohia te \left(512+5\sqrt{3}\right)\left(512-5\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}.

$$\frac{21\sqrt{15}\left(512-5\sqrt{3}\right)}{512^{2}-\left(5\sqrt{3}\right)^{2}}$$

Tātaihia te 512 mā te pū o 2, kia riro ko 262144.

$$\frac{21\sqrt{15}\left(512-5\sqrt{3}\right)}{262144-\left(5\sqrt{3}\right)^{2}}$$

Whakarohaina te \left(5\sqrt{3}\right)^{2}.

$$\frac{21\sqrt{15}\left(512-5\sqrt{3}\right)}{262144-5^{2}\left(\sqrt{3}\right)^{2}}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\frac{21\sqrt{15}\left(512-5\sqrt{3}\right)}{262144-25\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{21\sqrt{15}\left(512-5\sqrt{3}\right)}{262144-25\times 3}$$

Whakareatia te 25 ki te 3, ka 75.

$$\frac{21\sqrt{15}\left(512-5\sqrt{3}\right)}{262144-75}$$

Tangohia te 75 i te 262144, ka 262069.

$$\frac{21\sqrt{15}\left(512-5\sqrt{3}\right)}{262069}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 21\sqrt{15} ki te 512-5\sqrt{3}.

$$\frac{10752\sqrt{15}-105\sqrt{3}\sqrt{15}}{262069}$$

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}.

$$\frac{10752\sqrt{15}-105\sqrt{3}\sqrt{3}\sqrt{5}}{262069}$$

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

$$\frac{10752\sqrt{15}-105\times 3\sqrt{5}}{262069}$$

Whakareatia te -105 ki te 3, ka -315.

$$\frac{10752\sqrt{15}-315\sqrt{5}}{262069}$$