Whakaoti i te frac{sqrt{59}*29-sqrt{5*29}}{sqrt{59*29}+sqrt{5*29}}

$$\frac { \sqrt { 59 } \cdot 29 - \sqrt { 5 \cdot 29 } } { \sqrt { 59 \cdot 29 } + \sqrt { 5 \cdot 29 } }$$

Aromātai

$$\frac{59\sqrt{29}+5-\sqrt{295}-\sqrt{8555}}{54}\approx 3.945479937$$

Ngā Upane Otinga

Whakareatia te 5 ki te 29, ka 145.

$$\frac{29\sqrt{59}-\sqrt{145}}{\sqrt{59\times 29}+\sqrt{5\times 29}}$$

Whakareatia te 59 ki te 29, ka 1711.

$$\frac{29\sqrt{59}-\sqrt{145}}{\sqrt{1711}+\sqrt{5\times 29}}$$

Whakareatia te 5 ki te 29, ka 145.

$$\frac{29\sqrt{59}-\sqrt{145}}{\sqrt{1711}+\sqrt{145}}$$

Whakangāwaritia te tauraro o \frac{29\sqrt{59}-\sqrt{145}}{\sqrt{1711}+\sqrt{145}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{1711}-\sqrt{145}.

$$\frac{\left(29\sqrt{59}-\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}{\left(\sqrt{1711}+\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}$$

Whakaarohia te \left(\sqrt{1711}+\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(29\sqrt{59}-\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}{\left(\sqrt{1711}\right)^{2}-\left(\sqrt{145}\right)^{2}}$$

Pūrua \sqrt{1711}. Pūrua \sqrt{145}.

$$\frac{\left(29\sqrt{59}-\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}{1711-145}$$

Tangohia te 145 i te 1711, ka 1566.

$$\frac{\left(29\sqrt{59}-\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}{1566}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 29\sqrt{59}-\sqrt{145} ki ia tau o \sqrt{1711}-\sqrt{145}.

$$\frac{29\sqrt{59}\sqrt{1711}-29\sqrt{59}\sqrt{145}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Tauwehea te 1711=59\times 29. Tuhia anō te pūtake rua o te hua \sqrt{59\times 29} hei hua o ngā pūtake rua \sqrt{59}\sqrt{29}.

$$\frac{29\sqrt{59}\sqrt{59}\sqrt{29}-29\sqrt{59}\sqrt{145}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Whakareatia te \sqrt{59} ki te \sqrt{59}, ka 59.

$$\frac{29\times 59\sqrt{29}-29\sqrt{59}\sqrt{145}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Whakareatia te 29 ki te 59, ka 1711.

$$\frac{1711\sqrt{29}-29\sqrt{59}\sqrt{145}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Hei whakarea \sqrt{59} me \sqrt{145}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{1711\sqrt{29}-29\sqrt{8555}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Hei whakarea \sqrt{145} me \sqrt{1711}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{1711\sqrt{29}-29\sqrt{8555}-\sqrt{248095}+\left(\sqrt{145}\right)^{2}}{1566}$$

Ko te pūrua o \sqrt{145} ko 145.

$$\frac{1711\sqrt{29}-29\sqrt{8555}-\sqrt{248095}+145}{1566}$$

Tauwehea te 248095=29^{2}\times 295. Tuhia anō te pūtake rua o te hua \sqrt{29^{2}\times 295} hei hua o ngā pūtake rua \sqrt{29^{2}}\sqrt{295}. Tuhia te pūtakerua o te 29^{2}.

$$\frac{1711\sqrt{29}-29\sqrt{8555}-29\sqrt{295}+145}{1566}$$