Whakaoti i te sqrt{{8/3-1/2-[(1+1/3)^2:4/3+frac{1}{5}]*frac{5}{46}+(2-frac{1}{4})}:frac{3}{5}}

$$\sqrt { \{ \frac { 8 } { 3 } - \frac { 1 } { 2 } - [ ( 1 + \frac { 1 } { 3 } ) ^ { 2 } : \frac { 4 } { 3 } + \frac { 1 } { 5 } ] \times \frac { 5 } { 46 } + ( 2 - \frac { 1 } { 4 } ) \} : \frac { 3 } { 5 } }$$

Aromātai

$$\frac{5}{2}=2.5$$

Ngā Upane Otinga

Tangohia te \frac{1}{2} i te \frac{8}{3}, ka \frac{13}{6}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\left(1+\frac{1}{3}\right)^{2}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Tāpirihia te 1 ki te \frac{1}{3}, ka \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\left(\frac{4}{3}\right)^{2}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Tātaihia te \frac{4}{3} mā te pū o 2, kia riro ko \frac{16}{9}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\frac{16}{9}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Whakawehe \frac{16}{9} ki te \frac{4}{3} mā te whakarea \frac{16}{9} ki te tau huripoki o \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{16}{9}\times \frac{3}{4}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Whakareatia te \frac{16}{9} ki te \frac{3}{4}, ka \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{4}{3}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Tāpirihia te \frac{4}{3} ki te \frac{1}{5}, ka \frac{23}{15}.

$$\sqrt{\frac{\frac{13}{6}-\frac{23}{15}\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Whakareatia te \frac{23}{15} ki te \frac{5}{46}, ka \frac{1}{6}.

$$\sqrt{\frac{\frac{13}{6}-\frac{1}{6}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Tangohia te \frac{1}{6} i te \frac{13}{6}, ka 2.

$$\sqrt{\frac{2+2-\frac{1}{4}}{\frac{3}{5}}}$$

Tāpirihia te 2 ki te 2, ka 4.

$$\sqrt{\frac{4-\frac{1}{4}}{\frac{3}{5}}}$$

Tangohia te \frac{1}{4} i te 4, ka \frac{15}{4}.

$$\sqrt{\frac{\frac{15}{4}}{\frac{3}{5}}}$$

Whakawehe \frac{15}{4} ki te \frac{3}{5} mā te whakarea \frac{15}{4} ki te tau huripoki o \frac{3}{5}.

$$\sqrt{\frac{15}{4}\times \frac{5}{3}}$$

Whakareatia te \frac{15}{4} ki te \frac{5}{3}, ka \frac{25}{4}.

$$\sqrt{\frac{25}{4}}$$

Tuhia anō te pūtake rua o te whakawehenga \frac{25}{4} hei whakawehenga o ngā pūtake rua \frac{\sqrt{25}}{\sqrt{4}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{5}{2}$$

Tauwehe

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$