Whakaoti i te =sqrt{1/20-1[55-(15)^2/20]}

$$= \sqrt { \frac { 1 } { 20 - 1 } [ 55 - \frac { ( 15 ) ^ { 2 } } { 20 } ] }$$

Aromātai

$$\frac{5\sqrt{133}}{38}\approx 1.517442447$$

Ngā Upane Otinga

Tangohia te 1 i te 20, ka 19.

$$\sqrt{\frac{1}{19}\left(55-\frac{15^{2}}{20}\right)}$$

Tātaihia te 15 mā te pū o 2, kia riro ko 225.

$$\sqrt{\frac{1}{19}\left(55-\frac{225}{20}\right)}$$

Whakahekea te hautanga \frac{225}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\frac{1}{19}\left(55-\frac{45}{4}\right)}$$

Me tahuri te 55 ki te hautau \frac{220}{4}.

$$\sqrt{\frac{1}{19}\left(\frac{220}{4}-\frac{45}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{220}{4} me \frac{45}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{1}{19}\times \frac{220-45}{4}}$$

Tangohia te 45 i te 220, ka 175.

$$\sqrt{\frac{1}{19}\times \frac{175}{4}}$$

Me whakarea te \frac{1}{19} ki te \frac{175}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{1\times 175}{19\times 4}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 175}{19\times 4}.

$$\sqrt{\frac{175}{76}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{175}{76}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{175}}{\sqrt{76}}.

$$\frac{\sqrt{175}}{\sqrt{76}}$$

Tauwehea te 175=5^{2}\times 7. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 7} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{7}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{5\sqrt{7}}{\sqrt{76}}$$

Tauwehea te 76=2^{2}\times 19. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 19} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{19}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{5\sqrt{7}}{2\sqrt{19}}$$

Whakangāwaritia te tauraro o \frac{5\sqrt{7}}{2\sqrt{19}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{19}.

$$\frac{5\sqrt{7}\sqrt{19}}{2\left(\sqrt{19}\right)^{2}}$$

Ko te pūrua o \sqrt{19} ko 19.

$$\frac{5\sqrt{7}\sqrt{19}}{2\times 19}$$

Hei whakarea \sqrt{7} me \sqrt{19}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{5\sqrt{133}}{2\times 19}$$

Whakareatia te 2 ki te 19, ka 38.

$$\frac{5\sqrt{133}}{38}$$