Whakaoti i te (sqrt{7}+sqrt{3})(sqrt{7}+4sqrt{3})

$$( \sqrt { 7 } + \sqrt { 3 } ) ( \sqrt { 7 } + 4 \sqrt { 3 } )$$

Aromātai

$$5\sqrt{21}+19\approx 41.912878475$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o \sqrt{7}+\sqrt{3} ki ia tau o \sqrt{7}+4\sqrt{3}.

$$\left(\sqrt{7}\right)^{2}+4\sqrt{7}\sqrt{3}+\sqrt{3}\sqrt{7}+4\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{7} ko 7.

$$7+4\sqrt{7}\sqrt{3}+\sqrt{3}\sqrt{7}+4\left(\sqrt{3}\right)^{2}$$

Hei whakarea \sqrt{7} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$7+4\sqrt{21}+\sqrt{3}\sqrt{7}+4\left(\sqrt{3}\right)^{2}$$

Hei whakarea \sqrt{3} me \sqrt{7}, whakareatia ngā tau i raro i te pūtake rua.

$$7+4\sqrt{21}+\sqrt{21}+4\left(\sqrt{3}\right)^{2}$$

Pahekotia te 4\sqrt{21} me \sqrt{21}, ka 5\sqrt{21}.

$$7+5\sqrt{21}+4\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$7+5\sqrt{21}+4\times 3$$

Whakareatia te 4 ki te 3, ka 12.

$$7+5\sqrt{21}+12$$

Tāpirihia te 7 ki te 12, ka 19.

$$19+5\sqrt{21}$$