Whakaoti i te {r}{2sqrt{20}-sqrt{5}}{+3sqrt{1/5}}

$$\left. \begin{array} { r } { 2 \sqrt { 20 } - \sqrt { 5 } } \\ { + 3 \sqrt { \frac { 1 } { 5 } } } \end{array} \right.$$

Aromātai

$$\frac{18\sqrt{5}}{5}\approx 8.049844719$$

Ngā Upane Otinga

Tauwehea te 20=2^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 5} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{5}. Tuhia te pūtakerua o te 2^{2}.

$$2\times 2\sqrt{5}-\sqrt{5}+3\sqrt{\frac{1}{5}}$$

Whakareatia te 2 ki te 2, ka 4.

$$4\sqrt{5}-\sqrt{5}+3\sqrt{\frac{1}{5}}$$

Pahekotia te 4\sqrt{5} me -\sqrt{5}, ka 3\sqrt{5}.

$$3\sqrt{5}+3\sqrt{\frac{1}{5}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{5}}.

$$3\sqrt{5}+3\times \frac{\sqrt{1}}{\sqrt{5}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$3\sqrt{5}+3\times \frac{1}{\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

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

Ko te pūrua o \sqrt{5} ko 5.

$$3\sqrt{5}+3\times \frac{\sqrt{5}}{5}$$

Tuhia te 3\times \frac{\sqrt{5}}{5} hei hautanga kotahi.

$$3\sqrt{5}+\frac{3\sqrt{5}}{5}$$

Pahekotia te 3\sqrt{5} me \frac{3\sqrt{5}}{5}, ka \frac{18}{5}\sqrt{5}.

$$\frac{18}{5}\sqrt{5}$$