Whakaoti i te (4)(3+sqrt{10})(sqrt{2}-sqrt{5})

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

Aromātai

$$-4\sqrt{5}-8\sqrt{2}\approx -20.257980409$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te 3+\sqrt{10}.

$$\left(12+4\sqrt{10}\right)\left(\sqrt{2}-\sqrt{5}\right)$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 12+4\sqrt{10} ki ia tau o \sqrt{2}-\sqrt{5}.

$$12\sqrt{2}-12\sqrt{5}+4\sqrt{10}\sqrt{2}-4\sqrt{10}\sqrt{5}$$

Tauwehea te 10=2\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2\times 5} hei hua o ngā pūtake rua \sqrt{2}\sqrt{5}.

$$12\sqrt{2}-12\sqrt{5}+4\sqrt{2}\sqrt{5}\sqrt{2}-4\sqrt{10}\sqrt{5}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$12\sqrt{2}-12\sqrt{5}+4\times 2\sqrt{5}-4\sqrt{10}\sqrt{5}$$

Whakareatia te 4 ki te 2, ka 8.

$$12\sqrt{2}-12\sqrt{5}+8\sqrt{5}-4\sqrt{10}\sqrt{5}$$

Pahekotia te -12\sqrt{5} me 8\sqrt{5}, ka -4\sqrt{5}.

$$12\sqrt{2}-4\sqrt{5}-4\sqrt{10}\sqrt{5}$$

Tauwehea te 10=5\times 2. Tuhia anō te pūtake rua o te hua \sqrt{5\times 2} hei hua o ngā pūtake rua \sqrt{5}\sqrt{2}.

$$12\sqrt{2}-4\sqrt{5}-4\sqrt{5}\sqrt{2}\sqrt{5}$$

Whakareatia te \sqrt{5} ki te \sqrt{5}, ka 5.

$$12\sqrt{2}-4\sqrt{5}-4\times 5\sqrt{2}$$

Whakareatia te -4 ki te 5, ka -20.

$$12\sqrt{2}-4\sqrt{5}-20\sqrt{2}$$

Pahekotia te 12\sqrt{2} me -20\sqrt{2}, ka -8\sqrt{2}.

$$-8\sqrt{2}-4\sqrt{5}$$