Whakaoti i te sqrt{(1/4)^2+(1/3)^2}=1/2+1/3

$$\sqrt { ( \frac { 1 } { 4 } ) ^ { 2 } + ( \frac { 1 } { 3 } ) ^ { 2 } } = \frac { 1 } { 2 } + \frac { 1 } { 3 }$$

Manatoko

Ngā Upane Otinga

Tātaihia te \frac{1}{4} mā te pū o 2, kia riro ko \frac{1}{16}.

$$\sqrt{\frac{1}{16}+\left(\frac{1}{3}\right)^{2}}=\frac{1}{2}+\frac{1}{3}$$

Tātaihia te \frac{1}{3} mā te pū o 2, kia riro ko \frac{1}{9}.

$$\sqrt{\frac{1}{16}+\frac{1}{9}}=\frac{1}{2}+\frac{1}{3}$$

Ko te maha noa iti rawa atu o 16 me 9 ko 144. Me tahuri \frac{1}{16} me \frac{1}{9} ki te hautau me te tautūnga 144.

$$\sqrt{\frac{9}{144}+\frac{16}{144}}=\frac{1}{2}+\frac{1}{3}$$

Tā te mea he rite te tauraro o \frac{9}{144} me \frac{16}{144}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{9+16}{144}}=\frac{1}{2}+\frac{1}{3}$$

Tāpirihia te 9 ki te 16, ka 25.

$$\sqrt{\frac{25}{144}}=\frac{1}{2}+\frac{1}{3}$$

Tuhia anō te pūtake rua o te whakawehenga \frac{25}{144} hei whakawehenga o ngā pūtake rua \frac{\sqrt{25}}{\sqrt{144}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{5}{12}=\frac{1}{2}+\frac{1}{3}$$

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri \frac{1}{2} me \frac{1}{3} ki te hautau me te tautūnga 6.

$$\frac{5}{12}=\frac{3}{6}+\frac{2}{6}$$

Tā te mea he rite te tauraro o \frac{3}{6} me \frac{2}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5}{12}=\frac{3+2}{6}$$

Tāpirihia te 3 ki te 2, ka 5.

$$\frac{5}{12}=\frac{5}{6}$$

Ko te maha noa iti rawa atu o 12 me 6 ko 12. Me tahuri \frac{5}{12} me \frac{5}{6} ki te hautau me te tautūnga 12.

$$\frac{5}{12}=\frac{10}{12}$$

Whakatauritea te \frac{5}{12} me te \frac{10}{12}.

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