Whakaoti i te (1/2sqrt{3}-4sqrt{5})^2=

$$( \frac { 1 } { 2 } \sqrt { 3 } - 4 \sqrt { 5 } ) ^ { 2 } =$$

Aromātai

$$\frac{323}{4}-4\sqrt{15}\approx 65.258066615$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\frac{1}{2}\sqrt{3}-4\sqrt{5}\right)^{2}.

$$\frac{1}{4}\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{1}{4}\times 3-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

Whakareatia te \frac{1}{4} ki te 3, ka \frac{3}{4}.

$$\frac{3}{4}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{15}+16\left(\sqrt{5}\right)^{2}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{3}{4}-4\sqrt{15}+16\times 5$$

Whakareatia te 16 ki te 5, ka 80.

$$\frac{3}{4}-4\sqrt{15}+80$$

Tāpirihia te \frac{3}{4} ki te 80, ka \frac{323}{4}.

$$\frac{323}{4}-4\sqrt{15}$$

Whakaroha

$$\frac{323}{4} - 4 \sqrt{15} = 65.258066615$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\frac{1}{2}\sqrt{3}-4\sqrt{5}\right)^{2}.

$$\frac{1}{4}\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{1}{4}\times 3-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

Whakareatia te \frac{1}{4} ki te 3, ka \frac{3}{4}.

$$\frac{3}{4}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{15}+16\left(\sqrt{5}\right)^{2}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{3}{4}-4\sqrt{15}+16\times 5$$

Whakareatia te 16 ki te 5, ka 80.

$$\frac{3}{4}-4\sqrt{15}+80$$

Tāpirihia te \frac{3}{4} ki te 80, ka \frac{323}{4}.

$$\frac{323}{4}-4\sqrt{15}$$