Whakaoti i te sqrt{[(21/2-1/6+0.2)*9]-11/4}=

$$\sqrt { [ ( 2 \frac { 1 } { 2 } - \frac { 1 } { 6 } + 0.2 ) \cdot 9 ] - \frac { 11 } { 4 } } =$$

Aromātai

$$\frac{\sqrt{2005}}{10}\approx 4.477722635$$

Ngā Upane Otinga

Whakareatia te 2 ki te 2, ka 4.

$$\sqrt{\left(\frac{4+1}{2}-\frac{1}{6}+0.2\right)\times 9-\frac{11}{4}}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\sqrt{\left(\frac{5}{2}-\frac{1}{6}+0.2\right)\times 9-\frac{11}{4}}$$

Ko te maha noa iti rawa atu o 2 me 6 ko 6. Me tahuri \frac{5}{2} me \frac{1}{6} ki te hautau me te tautūnga 6.

$$\sqrt{\left(\frac{15}{6}-\frac{1}{6}+0.2\right)\times 9-\frac{11}{4}}$$

Tā te mea he rite te tauraro o \frac{15}{6} me \frac{1}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\left(\frac{15-1}{6}+0.2\right)\times 9-\frac{11}{4}}$$

Tangohia te 1 i te 15, ka 14.

$$\sqrt{\left(\frac{14}{6}+0.2\right)\times 9-\frac{11}{4}}$$

Whakahekea te hautanga \frac{14}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{\left(\frac{7}{3}+0.2\right)\times 9-\frac{11}{4}}$$

Me tahuri ki tau ā-ira 0.2 ki te hautau \frac{2}{10}. Whakahekea te hautanga \frac{2}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{\left(\frac{7}{3}+\frac{1}{5}\right)\times 9-\frac{11}{4}}$$

Ko te maha noa iti rawa atu o 3 me 5 ko 15. Me tahuri \frac{7}{3} me \frac{1}{5} ki te hautau me te tautūnga 15.

$$\sqrt{\left(\frac{35}{15}+\frac{3}{15}\right)\times 9-\frac{11}{4}}$$

Tā te mea he rite te tauraro o \frac{35}{15} me \frac{3}{15}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{35+3}{15}\times 9-\frac{11}{4}}$$

Tāpirihia te 35 ki te 3, ka 38.

$$\sqrt{\frac{38}{15}\times 9-\frac{11}{4}}$$

Tuhia te \frac{38}{15}\times 9 hei hautanga kotahi.

$$\sqrt{\frac{38\times 9}{15}-\frac{11}{4}}$$

Whakareatia te 38 ki te 9, ka 342.

$$\sqrt{\frac{342}{15}-\frac{11}{4}}$$

Whakahekea te hautanga \frac{342}{15} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{\frac{114}{5}-\frac{11}{4}}$$

Ko te maha noa iti rawa atu o 5 me 4 ko 20. Me tahuri \frac{114}{5} me \frac{11}{4} ki te hautau me te tautūnga 20.

$$\sqrt{\frac{456}{20}-\frac{55}{20}}$$

Tā te mea he rite te tauraro o \frac{456}{20} me \frac{55}{20}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{456-55}{20}}$$

Tangohia te 55 i te 456, ka 401.

$$\sqrt{\frac{401}{20}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{401}{20}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{401}}{\sqrt{20}}.

$$\frac{\sqrt{401}}{\sqrt{20}}$$

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}.

$$\frac{\sqrt{401}}{2\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{401}}{2\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{\sqrt{401}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{\sqrt{401}\sqrt{5}}{2\times 5}$$

Hei whakarea \sqrt{401} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{2005}}{2\times 5}$$

Whakareatia te 2 ki te 5, ka 10.

$$\frac{\sqrt{2005}}{10}$$