Whakaoti i te 4sqrt{15/8}u1/5sqrt{750}

$$4 \sqrt { \frac { 15 } { 8 } } u \frac { 1 } { 5 } \sqrt { 750 }$$

Aromātai

$$30u$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{15}{8}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{15}}{\sqrt{8}}.

$$4\times \frac{\sqrt{15}}{\sqrt{8}}u\times \frac{1}{5}\sqrt{750}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$4\times \frac{\sqrt{15}}{2\sqrt{2}}u\times \frac{1}{5}\sqrt{750}$$

Whakangāwaritia te tauraro o \frac{\sqrt{15}}{2\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$4\times \frac{\sqrt{15}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}u\times \frac{1}{5}\sqrt{750}$$

Ko te pūrua o \sqrt{2} ko 2.

$$4\times \frac{\sqrt{15}\sqrt{2}}{2\times 2}u\times \frac{1}{5}\sqrt{750}$$

Hei whakarea \sqrt{15} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$4\times \frac{\sqrt{30}}{2\times 2}u\times \frac{1}{5}\sqrt{750}$$

Whakareatia te 2 ki te 2, ka 4.

$$4\times \frac{\sqrt{30}}{4}u\times \frac{1}{5}\sqrt{750}$$

Whakareatia te 4 ki te \frac{1}{5}, ka \frac{4}{5}.

$$\frac{4}{5}\times \frac{\sqrt{30}}{4}u\sqrt{750}$$

Tauwehea te 750=5^{2}\times 30. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 30} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{30}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{4}{5}\times \frac{\sqrt{30}}{4}u\times 5\sqrt{30}$$

Me whakakore te 5 me te 5.

$$4\times \frac{\sqrt{30}}{4}u\sqrt{30}$$

Me whakakore te 4 me te 4.

$$\sqrt{30}u\sqrt{30}$$

Whakareatia te \sqrt{30} ki te \sqrt{30}, ka 30.

$$30u$$

Kimi Pārōnaki e ai ki u

$$30$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{15}{8}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{15}}{\sqrt{8}}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{15}}{\sqrt{8}}u\times \frac{1}{5}\sqrt{750})$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{15}}{2\sqrt{2}}u\times \frac{1}{5}\sqrt{750})$$

Whakangāwaritia te tauraro o \frac{\sqrt{15}}{2\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{15}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}u\times \frac{1}{5}\sqrt{750})$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{15}\sqrt{2}}{2\times 2}u\times \frac{1}{5}\sqrt{750})$$

Hei whakarea \sqrt{15} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{30}}{2\times 2}u\times \frac{1}{5}\sqrt{750})$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{30}}{4}u\times \frac{1}{5}\sqrt{750})$$

Whakareatia te 4 ki te \frac{1}{5}, ka \frac{4}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{4}{5}\times \frac{\sqrt{30}}{4}u\sqrt{750})$$

Tauwehea te 750=5^{2}\times 30. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 30} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{30}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{4}{5}\times \frac{\sqrt{30}}{4}u\times 5\sqrt{30})$$

Me whakakore te 5 me te 5.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{30}}{4}u\sqrt{30})$$

Me whakakore te 4 me te 4.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\sqrt{30}u\sqrt{30})$$

Whakareatia te \sqrt{30} ki te \sqrt{30}, ka 30.

$$\frac{\mathrm{d}}{\mathrm{d}u}(30u)$$

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

$$30u^{1-1}$$

Tango 1 mai i 1.

$$30u^{0}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$30\times 1$$

Mō tētahi kupu t, t\times 1=t me 1t=t.

$$30$$