Whakaoti i te sqrt{18^2+(144/sqrt{3})^2}=

$$\sqrt { 18 ^ { 2 } + ( \frac { 144 } { \sqrt { 3 } } ) ^ { 2 } } =$$

Aromātai

$$6\sqrt{201}\approx 85.064681273$$

Ngā Upane Otinga

Tātaihia te 18 mā te pū o 2, kia riro ko 324.

$$\sqrt{324+\left(\frac{144}{\sqrt{3}}\right)^{2}}$$

Whakangāwaritia te tauraro o \frac{144}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\sqrt{324+\left(\frac{144\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\sqrt{324+\left(\frac{144\sqrt{3}}{3}\right)^{2}}$$

Whakawehea te 144\sqrt{3} ki te 3, kia riro ko 48\sqrt{3}.

$$\sqrt{324+\left(48\sqrt{3}\right)^{2}}$$

Whakarohaina te \left(48\sqrt{3}\right)^{2}.

$$\sqrt{324+48^{2}\left(\sqrt{3}\right)^{2}}$$

Tātaihia te 48 mā te pū o 2, kia riro ko 2304.

$$\sqrt{324+2304\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\sqrt{324+2304\times 3}$$

Whakareatia te 2304 ki te 3, ka 6912.

$$\sqrt{324+6912}$$

Tāpirihia te 324 ki te 6912, ka 7236.

$$\sqrt{7236}$$

Tauwehea te 7236=6^{2}\times 201. Tuhia anō te pūtake rua o te hua \sqrt{6^{2}\times 201} hei hua o ngā pūtake rua \sqrt{6^{2}}\sqrt{201}. Tuhia te pūtakerua o te 6^{2}.

$$6\sqrt{201}$$