Whakaoti i te frac{sqrt{56^2-46^2}}{0,25*sqrt{10}}

$$\frac { \sqrt { 56 ^ { 2 } - 46 ^ { 2 } } } { 0,25 \cdot \sqrt { 10 } }$$

Aromātai

$$4\sqrt{102}\approx 40.398019753$$

Ngā Upane Otinga

Tātaihia te 56 mā te pū o 2, kia riro ko 3136.

$$\frac{\sqrt{3136-46^{2}}}{0.25\sqrt{10}}$$

Tātaihia te 46 mā te pū o 2, kia riro ko 2116.

$$\frac{\sqrt{3136-2116}}{0.25\sqrt{10}}$$

Tangohia te 2116 i te 3136, ka 1020.

$$\frac{\sqrt{1020}}{0.25\sqrt{10}}$$

Tauwehea te 1020=2^{2}\times 255. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 255} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{255}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{2\sqrt{255}}{0.25\sqrt{10}}$$

Whakangāwaritia te tauraro o \frac{2\sqrt{255}}{0.25\sqrt{10}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{10}.

$$\frac{2\sqrt{255}\sqrt{10}}{0.25\left(\sqrt{10}\right)^{2}}$$

Ko te pūrua o \sqrt{10} ko 10.

$$\frac{2\sqrt{255}\sqrt{10}}{0.25\times 10}$$

Hei whakarea \sqrt{255} me \sqrt{10}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{2\sqrt{2550}}{0.25\times 10}$$

Whakareatia te 0.25 ki te 10, ka 2.5.

$$\frac{2\sqrt{2550}}{2.5}$$

Tauwehea te 2550=5^{2}\times 102. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 102} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{102}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{2\times 5\sqrt{102}}{2.5}$$

Whakareatia te 2 ki te 5, ka 10.

$$\frac{10\sqrt{102}}{2.5}$$

Whakawehea te 10\sqrt{102} ki te 2.5, kia riro ko 4\sqrt{102}.

$$4\sqrt{102}$$