Whakaoti i te sqrt{[4/13*(7-1/5*75/4)]:[16/3*(frac{4}{3}+frac{5}{6}:frac{1}{2})]}+sqrt{(frac{53}{5}-frac{63}{20}-5)*(1+frac{1}{4})}

$$\sqrt { [ \frac { 4 } { 13 } \times ( 7 - \frac { 1 } { 5 } \times \frac { 75 } { 4 } ) ] : [ \frac { 16 } { 3 } \times ( \frac { 4 } { 3 } + \frac { 5 } { 6 } : \frac { 1 } { 2 } ) ] } + \sqrt { ( \frac { 53 } { 5 } - \frac { 63 } { 20 } - 5 ) \times ( 1 + \frac { 1 } { 4 } ) }$$

Aromātai

$$2$$

Ngā Upane Otinga

Me whakarea te \frac{1}{5} ki te \frac{75}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{\frac{4}{13}\left(7-\frac{1\times 75}{5\times 4}\right)}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 75}{5\times 4}.

$$\sqrt{\frac{\frac{4}{13}\left(7-\frac{75}{20}\right)}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Whakahekea te hautanga \frac{75}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\frac{\frac{4}{13}\left(7-\frac{15}{4}\right)}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Me tahuri te 7 ki te hautau \frac{28}{4}.

$$\sqrt{\frac{\frac{4}{13}\left(\frac{28}{4}-\frac{15}{4}\right)}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{28}{4} me \frac{15}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{\frac{4}{13}\times \frac{28-15}{4}}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Tangohia te 15 i te 28, ka 13.

$$\sqrt{\frac{\frac{4}{13}\times \frac{13}{4}}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Me whakakore atu te \frac{4}{13} me tōna tau utu \frac{13}{4}.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Whakawehe \frac{5}{6} ki te \frac{1}{2} mā te whakarea \frac{5}{6} ki te tau huripoki o \frac{1}{2}.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{5}{6}\times 2\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Tuhia te \frac{5}{6}\times 2 hei hautanga kotahi.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{5\times 2}{6}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Whakareatia te 5 ki te 2, ka 10.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{10}{6}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Whakahekea te hautanga \frac{10}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{5}{3}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{4}{3} me \frac{5}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{1}{\frac{16}{3}\times \frac{4+5}{3}}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Tāpirihia te 4 ki te 5, ka 9.

$$\sqrt{\frac{1}{\frac{16}{3}\times \frac{9}{3}}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Whakawehea te 9 ki te 3, kia riro ko 3.

$$\sqrt{\frac{1}{\frac{16}{3}\times 3}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Me whakakore te 3 me te 3.

$$\sqrt{\frac{1}{16}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Tuhia anō te pūtake rua o te whakawehenga \frac{1}{16} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{16}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{1}{4}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Ko te maha noa iti rawa atu o 5 me 20 ko 20. Me tahuri \frac{53}{5} me \frac{63}{20} ki te hautau me te tautūnga 20.

$$\frac{1}{4}+\sqrt{\left(\frac{212}{20}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{212}{20} me \frac{63}{20}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{4}+\sqrt{\left(\frac{212-63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Tangohia te 63 i te 212, ka 149.

$$\frac{1}{4}+\sqrt{\left(\frac{149}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

Me tahuri te 5 ki te hautau \frac{100}{20}.

$$\frac{1}{4}+\sqrt{\left(\frac{149}{20}-\frac{100}{20}\right)\left(1+\frac{1}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{149}{20} me \frac{100}{20}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{4}+\sqrt{\frac{149-100}{20}\left(1+\frac{1}{4}\right)}$$

Tangohia te 100 i te 149, ka 49.

$$\frac{1}{4}+\sqrt{\frac{49}{20}\left(1+\frac{1}{4}\right)}$$

Me tahuri te 1 ki te hautau \frac{4}{4}.

$$\frac{1}{4}+\sqrt{\frac{49}{20}\left(\frac{4}{4}+\frac{1}{4}\right)}$$

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

$$\frac{1}{4}+\sqrt{\frac{49}{20}\times \frac{4+1}{4}}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{1}{4}+\sqrt{\frac{49}{20}\times \frac{5}{4}}$$

Me whakarea te \frac{49}{20} ki te \frac{5}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1}{4}+\sqrt{\frac{49\times 5}{20\times 4}}$$

Mahia ngā whakarea i roto i te hautanga \frac{49\times 5}{20\times 4}.

$$\frac{1}{4}+\sqrt{\frac{245}{80}}$$

Whakahekea te hautanga \frac{245}{80} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{1}{4}+\sqrt{\frac{49}{16}}$$

Tuhia anō te pūtake rua o te whakawehenga \frac{49}{16} hei whakawehenga o ngā pūtake rua \frac{\sqrt{49}}{\sqrt{16}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{1}{4}+\frac{7}{4}$$

Tā te mea he rite te tauraro o \frac{1}{4} me \frac{7}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1+7}{4}$$

Tāpirihia te 1 ki te 7, ka 8.

$$\frac{8}{4}$$

Whakawehea te 8 ki te 4, kia riro ko 2.

$$2$$

Tauwehe

$$2$$