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

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

Aromātai

$$4-9\sqrt{6}\approx -18.045407685$$

Ngā Upane Otinga

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

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

Ko te pūrua o \sqrt{2} ko 2.

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

Whakareatia te 5 ki te 2, ka 10.

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

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

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

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

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

Pahekotia te -10\sqrt{6} me \sqrt{6}, ka -9\sqrt{6}.

$$10-9\sqrt{6}-2\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$10-9\sqrt{6}-2\times 3$$

Whakareatia te -2 ki te 3, ka -6.

$$10-9\sqrt{6}-6$$

Tangohia te 6 i te 10, ka 4.

$$4-9\sqrt{6}$$