Whakaoti i te 5sqrt{25^2-7^2/27}

$$5 \sqrt { \frac { 25 ^ { 2 } - 7 ^ { 2 } } { 27 } }$$

Aromātai

$$\frac{40\sqrt{3}}{3}\approx 23.094010768$$

Ngā Upane Otinga

Tātaihia te 25 mā te pū o 2, kia riro ko 625.

$$5\sqrt{\frac{625-7^{2}}{27}}$$

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$5\sqrt{\frac{625-49}{27}}$$

Tangohia te 49 i te 625, ka 576.

$$5\sqrt{\frac{576}{27}}$$

Whakahekea te hautanga \frac{576}{27} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$5\sqrt{\frac{64}{3}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{64}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{64}}{\sqrt{3}}.

$$5\times \frac{\sqrt{64}}{\sqrt{3}}$$

Tātaitia te pūtakerua o 64 kia tae ki 8.

$$5\times \frac{8}{\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{8}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$5\times \frac{8\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$5\times \frac{8\sqrt{3}}{3}$$

Tuhia te 5\times \frac{8\sqrt{3}}{3} hei hautanga kotahi.

$$\frac{5\times 8\sqrt{3}}{3}$$

Whakareatia te 5 ki te 8, ka 40.

$$\frac{40\sqrt{3}}{3}$$