Whakaoti i te 1/sqrt{5+2}+1/3sqrt{8}

$$\frac{ 1 }{ \sqrt{ 5+2 } } + \frac{ 1 }{ 3 \sqrt{ 8 } }$$

Aromātai

$$\frac{\sqrt{7}\left(\sqrt{14}+12\right)}{84}\approx 0.495815603$$

Ngā Hipanga Rongoā Poto

Tāpirihia te 5 ki te 2, ka 7.

$$\frac{1}{\sqrt{7}}+\frac{1}{3\sqrt{8}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{7}.

$$\frac{\sqrt{7}}{\left(\sqrt{7}\right)^{2}}+\frac{1}{3\sqrt{8}}$$

Ko te pūrua o \sqrt{7} ko 7.

$$\frac{\sqrt{7}}{7}+\frac{1}{3\sqrt{8}}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{\sqrt{7}}{7}+\frac{1}{3\times 2\sqrt{2}}$$

Whakareatia te 3 ki te 2, ka 6.

$$\frac{\sqrt{7}}{7}+\frac{1}{6\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{1}{6\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{\sqrt{7}}{7}+\frac{\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\sqrt{7}}{7}+\frac{\sqrt{2}}{6\times 2}$$

Whakareatia te 6 ki te 2, ka 12.

$$\frac{\sqrt{7}}{7}+\frac{\sqrt{2}}{12}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 7 me 12 ko 84. Whakareatia \frac{\sqrt{7}}{7} ki te \frac{12}{12}. Whakareatia \frac{\sqrt{2}}{12} ki te \frac{7}{7}.

$$\frac{12\sqrt{7}}{84}+\frac{7\sqrt{2}}{84}$$

Tā te mea he rite te tauraro o \frac{12\sqrt{7}}{84} me \frac{7\sqrt{2}}{84}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{12\sqrt{7}+7\sqrt{2}}{84}$$

Tauwehe

$$\frac{\sqrt{7} {(\sqrt{2} \sqrt{7} + 12)}}{84} = 0.49581560320698514$$