Whakaoti i te sqrt{3(2-5)^2+(7-4(2)^3/3)}

$$\sqrt { 3 ( 2 - 5 ) ^ { 2 } + ( \frac { 7 - 4 ( 2 ) ^ { 3 } } { 3 } ) }$$

Aromātai

$$\frac{2\sqrt{42}}{3}\approx 4.320493799$$

Ngā Upane Otinga

Tangohia te 5 i te 2, ka -3.

$$\sqrt{3\left(-3\right)^{2}+\frac{7-4\times 2^{3}}{3}}$$

Tātaihia te -3 mā te pū o 2, kia riro ko 9.

$$\sqrt{3\times 9+\frac{7-4\times 2^{3}}{3}}$$

Whakareatia te 3 ki te 9, ka 27.

$$\sqrt{27+\frac{7-4\times 2^{3}}{3}}$$

Tātaihia te 2 mā te pū o 3, kia riro ko 8.

$$\sqrt{27+\frac{7-4\times 8}{3}}$$

Whakareatia te 4 ki te 8, ka 32.

$$\sqrt{27+\frac{7-32}{3}}$$

Tangohia te 32 i te 7, ka -25.

$$\sqrt{27+\frac{-25}{3}}$$

Ka taea te hautanga \frac{-25}{3} te tuhi anō ko -\frac{25}{3} mā te tango i te tohu tōraro.

$$\sqrt{27-\frac{25}{3}}$$

Tangohia te \frac{25}{3} i te 27, ka \frac{56}{3}.

$$\sqrt{\frac{56}{3}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{56}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{56}}{\sqrt{3}}.

$$\frac{\sqrt{56}}{\sqrt{3}}$$

Tauwehea te 56=2^{2}\times 14. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 14} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{14}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{2\sqrt{14}}{\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{2\sqrt{14}}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{2\sqrt{14}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{2\sqrt{14}\sqrt{3}}{3}$$

Hei whakarea \sqrt{14} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{2\sqrt{42}}{3}$$