Whakaoti i te sqrt{(5/2)^2+25/3}

$$\sqrt { ( \frac { 5 } { 2 } ) ^ { 2 } + \frac { 25 } { 3 } }$$

Aromātai

$$\frac{5\sqrt{21}}{6}\approx 3.818813079$$

Ngā Upane Otinga

Tātaihia te \frac{5}{2} mā te pū o 2, kia riro ko \frac{25}{4}.

$$\sqrt{\frac{25}{4}+\frac{25}{3}}$$

Ko te maha noa iti rawa atu o 4 me 3 ko 12. Me tahuri \frac{25}{4} me \frac{25}{3} ki te hautau me te tautūnga 12.

$$\sqrt{\frac{75}{12}+\frac{100}{12}}$$

Tā te mea he rite te tauraro o \frac{75}{12} me \frac{100}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{75+100}{12}}$$

Tāpirihia te 75 ki te 100, ka 175.

$$\sqrt{\frac{175}{12}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{175}{12}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{175}}{\sqrt{12}}.

$$\frac{\sqrt{175}}{\sqrt{12}}$$

Tauwehea te 175=5^{2}\times 7. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 7} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{7}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{5\sqrt{7}}{\sqrt{12}}$$

Tauwehea te 12=2^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 3} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{3}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{5\sqrt{7}}{2\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{5\sqrt{7}}{2\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{5\sqrt{7}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{5\sqrt{7}\sqrt{3}}{2\times 3}$$

Hei whakarea \sqrt{7} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{5\sqrt{21}}{2\times 3}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{5\sqrt{21}}{6}$$