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

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

Aromātai

$$7-\sqrt{15}\approx 3.127016654$$

Ngā Upane Otinga

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

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

Ko te pūrua o \sqrt{5} ko 5.

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

Whakareatia te 2 ki te 5, ka 10.

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

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

$$10-2\sqrt{15}+\sqrt{3}\sqrt{5}-\left(\sqrt{3}\right)^{2}$$

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

$$10-2\sqrt{15}+\sqrt{15}-\left(\sqrt{3}\right)^{2}$$

Pahekotia te -2\sqrt{15} me \sqrt{15}, ka -\sqrt{15}.

$$10-\sqrt{15}-\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$10-\sqrt{15}-3$$

Tangohia te 3 i te 10, ka 7.

$$7-\sqrt{15}$$