Whakaoti i te (2sqrt{3}+3sqrt{5})*(2sqrt{3}-3sqrt{5})

$$(2 \sqrt{ 3 } +3 \sqrt{ 5 } ) \times (2 \sqrt{ 3 } -3 \sqrt{ 5 } )$$

Aromātai

$$-33$$

Ngā Upane Otinga

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}.

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

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

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Ko te pūrua o \sqrt{3} ko 3.

$$4\times 3-\left(3\sqrt{5}\right)^{2}$$

Whakareatia te 4 ki te 3, ka 12.

$$12-\left(3\sqrt{5}\right)^{2}$$

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

$$12-3^{2}\left(\sqrt{5}\right)^{2}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$12-9\left(\sqrt{5}\right)^{2}$$

Ko te pūrua o \sqrt{5} ko 5.

$$12-9\times 5$$

Whakareatia te 9 ki te 5, ka 45.

$$12-45$$

Tangohia te 45 i te 12, ka -33.

$$-33$$

Tauwehe

$$-33$$