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

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

Aromātai

$$26-9\sqrt{6}\approx 3.954592315$$

Ngā Upane Otinga

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

$$2\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{2}-5\sqrt{2}\sqrt{3}+10\left(\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$2\times 3-4\sqrt{3}\sqrt{2}-5\sqrt{2}\sqrt{3}+10\left(\sqrt{2}\right)^{2}$$

Whakareatia te 2 ki te 3, ka 6.

$$6-4\sqrt{3}\sqrt{2}-5\sqrt{2}\sqrt{3}+10\left(\sqrt{2}\right)^{2}$$

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

$$6-4\sqrt{6}-5\sqrt{2}\sqrt{3}+10\left(\sqrt{2}\right)^{2}$$

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

$$6-4\sqrt{6}-5\sqrt{6}+10\left(\sqrt{2}\right)^{2}$$

Pahekotia te -4\sqrt{6} me -5\sqrt{6}, ka -9\sqrt{6}.

$$6-9\sqrt{6}+10\left(\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$6-9\sqrt{6}+10\times 2$$

Whakareatia te 10 ki te 2, ka 20.

$$6-9\sqrt{6}+20$$

Tāpirihia te 6 ki te 20, ka 26.

$$26-9\sqrt{6}$$

Tauwehe

$$26-9\sqrt{6}$$