Whakaoti i te (3sqrt{5}+2sqrt{3})(7sqrt{2}-sqrt{5})

$$( 3 \sqrt { 5 } + 2 \sqrt { 3 } ) ( 7 \sqrt { 2 } - \sqrt { 5 } )$$

Aromātai

$$14\sqrt{6}+21\sqrt{10}-2\sqrt{15}-15\approx 77.95472057$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 3\sqrt{5}+2\sqrt{3} ki ia tau o 7\sqrt{2}-\sqrt{5}.

$$21\sqrt{5}\sqrt{2}-3\left(\sqrt{5}\right)^{2}+14\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{5}$$

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

$$21\sqrt{10}-3\left(\sqrt{5}\right)^{2}+14\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{5}$$

Ko te pūrua o \sqrt{5} ko 5.

$$21\sqrt{10}-3\times 5+14\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{5}$$

Whakareatia te -3 ki te 5, ka -15.

$$21\sqrt{10}-15+14\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{5}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$21\sqrt{10}-15+14\sqrt{6}-2\sqrt{3}\sqrt{5}$$

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

$$21\sqrt{10}-15+14\sqrt{6}-2\sqrt{15}$$

Tauwehe

$$14 \sqrt{6} + 21 \sqrt{10} - 2 \sqrt{15} - 15 = 77.95472057$$