Whakaoti i te sqrt{{[(10/3-11/6)*4/15+3/5*(frac{2}{3}-frac{1}{2})]:frac{8}{3}+1-(frac{1}{2})^2}*(3+frac{3}{4})}

$$\sqrt { \{ [ ( \frac { 10 } { 3 } - \frac { 11 } { 6 } ) \times \frac { 4 } { 15 } + \frac { 3 } { 5 } \times ( \frac { 2 } { 3 } - \frac { 1 } { 2 } ) ] : \frac { 8 } { 3 } + 1 - ( \frac { 1 } { 2 } ) ^ { 2 } \} \times ( 3 + \frac { 3 } { 4 } ) }$$

Aromātai

$$\frac{15}{8}=1.875$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 3 me 6 ko 6. Me tahuri \frac{10}{3} me \frac{11}{6} ki te hautau me te tautūnga 6.

$$\sqrt{\left(\frac{\left(\frac{20}{6}-\frac{11}{6}\right)\times \frac{4}{15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{20}{6} me \frac{11}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\left(\frac{\frac{20-11}{6}\times \frac{4}{15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Tangohia te 11 i te 20, ka 9.

$$\sqrt{\left(\frac{\frac{9}{6}\times \frac{4}{15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Whakahekea te hautanga \frac{9}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{\left(\frac{\frac{3}{2}\times \frac{4}{15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Me whakarea te \frac{3}{2} ki te \frac{4}{15} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\left(\frac{\frac{3\times 4}{2\times 15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 4}{2\times 15}.

$$\sqrt{\left(\frac{\frac{12}{30}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Whakahekea te hautanga \frac{12}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Ko te maha noa iti rawa atu o 3 me 2 ko 6. Me tahuri \frac{2}{3} me \frac{1}{2} ki te hautau me te tautūnga 6.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{5}\left(\frac{4}{6}-\frac{3}{6}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{4}{6} me \frac{3}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{5}\times \frac{4-3}{6}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Tangohia te 3 i te 4, ka 1.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{5}\times \frac{1}{6}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Me whakarea te \frac{3}{5} ki te \frac{1}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3\times 1}{5\times 6}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 1}{5\times 6}.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{30}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Whakahekea te hautanga \frac{3}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{1}{10}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Ko te maha noa iti rawa atu o 5 me 10 ko 10. Me tahuri \frac{2}{5} me \frac{1}{10} ki te hautau me te tautūnga 10.

$$\sqrt{\left(\frac{\frac{4}{10}+\frac{1}{10}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{4}{10} me \frac{1}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\left(\frac{\frac{4+1}{10}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\sqrt{\left(\frac{\frac{5}{10}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Whakahekea te hautanga \frac{5}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\left(\frac{\frac{1}{2}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Whakawehe \frac{1}{2} ki te \frac{8}{3} mā te whakarea \frac{1}{2} ki te tau huripoki o \frac{8}{3}.

$$\sqrt{\left(\frac{1}{2}\times \frac{3}{8}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Me whakarea te \frac{1}{2} ki te \frac{3}{8} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\left(\frac{1\times 3}{2\times 8}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 3}{2\times 8}.

$$\sqrt{\left(\frac{3}{16}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Me tahuri te 1 ki te hautau \frac{16}{16}.

$$\sqrt{\left(\frac{3}{16}+\frac{16}{16}-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{3}{16} me \frac{16}{16}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\left(\frac{3+16}{16}-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Tāpirihia te 3 ki te 16, ka 19.

$$\sqrt{\left(\frac{19}{16}-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Tātaihia te \frac{1}{2} mā te pū o 2, kia riro ko \frac{1}{4}.

$$\sqrt{\left(\frac{19}{16}-\frac{1}{4}\right)\left(3+\frac{3}{4}\right)}$$

Ko te maha noa iti rawa atu o 16 me 4 ko 16. Me tahuri \frac{19}{16} me \frac{1}{4} ki te hautau me te tautūnga 16.

$$\sqrt{\left(\frac{19}{16}-\frac{4}{16}\right)\left(3+\frac{3}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{19}{16} me \frac{4}{16}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{19-4}{16}\left(3+\frac{3}{4}\right)}$$

Tangohia te 4 i te 19, ka 15.

$$\sqrt{\frac{15}{16}\left(3+\frac{3}{4}\right)}$$

Me tahuri te 3 ki te hautau \frac{12}{4}.

$$\sqrt{\frac{15}{16}\left(\frac{12}{4}+\frac{3}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{12}{4} me \frac{3}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{15}{16}\times \frac{12+3}{4}}$$

Tāpirihia te 12 ki te 3, ka 15.

$$\sqrt{\frac{15}{16}\times \frac{15}{4}}$$

Me whakarea te \frac{15}{16} ki te \frac{15}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{15\times 15}{16\times 4}}$$

Mahia ngā whakarea i roto i te hautanga \frac{15\times 15}{16\times 4}.

$$\sqrt{\frac{225}{64}}$$

Tuhia anō te pūtake rua o te whakawehenga \frac{225}{64} hei whakawehenga o ngā pūtake rua \frac{\sqrt{225}}{\sqrt{64}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{15}{8}$$

Tauwehe

$$\frac{3 \cdot 5}{2 ^ {3}} = 1\frac{7}{8} = 1.875$$