Whakaoti i te sqrt{3/2*(5/4-10/9)+1/16-(frac{1}{2}-frac{7}{18}):frac{16}{3}}=

$$\sqrt { \frac { 3 } { 2 } \cdot ( \frac { 5 } { 4 } - \frac { 10 } { 9 } ) + \frac { 1 } { 16 } - ( \frac { 1 } { 2 } - \frac { 7 } { 18 } ) : \frac { 16 } { 3 } } =$$

Aromātai

$$\frac{1}{2}=0.5$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 4 me 9 ko 36. Me tahuri \frac{5}{4} me \frac{10}{9} ki te hautau me te tautūnga 36.

$$\sqrt{\frac{3}{2}\left(\frac{45}{36}-\frac{40}{36}\right)+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Tā te mea he rite te tauraro o \frac{45}{36} me \frac{40}{36}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{3}{2}\times \frac{45-40}{36}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Tangohia te 40 i te 45, ka 5.

$$\sqrt{\frac{3}{2}\times \frac{5}{36}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Me whakarea te \frac{3}{2} ki te \frac{5}{36} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{3\times 5}{2\times 36}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 5}{2\times 36}.

$$\sqrt{\frac{15}{72}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Whakahekea te hautanga \frac{15}{72} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{\frac{5}{24}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Ko te maha noa iti rawa atu o 24 me 16 ko 48. Me tahuri \frac{5}{24} me \frac{1}{16} ki te hautau me te tautūnga 48.

$$\sqrt{\frac{10}{48}+\frac{3}{48}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Tā te mea he rite te tauraro o \frac{10}{48} me \frac{3}{48}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{10+3}{48}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Tāpirihia te 10 ki te 3, ka 13.

$$\sqrt{\frac{13}{48}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Ko te maha noa iti rawa atu o 2 me 18 ko 18. Me tahuri \frac{1}{2} me \frac{7}{18} ki te hautau me te tautūnga 18.

$$\sqrt{\frac{13}{48}-\frac{\frac{9}{18}-\frac{7}{18}}{\frac{16}{3}}}$$

Tā te mea he rite te tauraro o \frac{9}{18} me \frac{7}{18}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{13}{48}-\frac{\frac{9-7}{18}}{\frac{16}{3}}}$$

Tangohia te 7 i te 9, ka 2.

$$\sqrt{\frac{13}{48}-\frac{\frac{2}{18}}{\frac{16}{3}}}$$

Whakahekea te hautanga \frac{2}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{\frac{13}{48}-\frac{\frac{1}{9}}{\frac{16}{3}}}$$

Whakawehe \frac{1}{9} ki te \frac{16}{3} mā te whakarea \frac{1}{9} ki te tau huripoki o \frac{16}{3}.

$$\sqrt{\frac{13}{48}-\frac{1}{9}\times \frac{3}{16}}$$

Me whakarea te \frac{1}{9} ki te \frac{3}{16} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{13}{48}-\frac{1\times 3}{9\times 16}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 3}{9\times 16}.

$$\sqrt{\frac{13}{48}-\frac{3}{144}}$$

Whakahekea te hautanga \frac{3}{144} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{\frac{13}{48}-\frac{1}{48}}$$

Tā te mea he rite te tauraro o \frac{13}{48} me \frac{1}{48}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{13-1}{48}}$$

Tangohia te 1 i te 13, ka 12.

$$\sqrt{\frac{12}{48}}$$

Whakahekea te hautanga \frac{12}{48} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$\sqrt{\frac{1}{4}}$$

Tuhia anō te pūtake rua o te whakawehenga \frac{1}{4} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{4}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{1}{2}$$

Tauwehe

$$\frac{1}{2} = 0.5$$