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

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

Aromātai

$$-\sqrt{15}-1\approx -4.872983346$$

Ngā Upane Otinga

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

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

Ko te pūrua o \sqrt{5} ko 5.

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

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

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

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

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

$$5-\sqrt{15}-2\times 3$$

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

$$5-\sqrt{15}-6$$

Tangohia te 6 i te 5, ka -1.

$$-1-\sqrt{15}$$