Whakaoti i te sqrt{0.1(-14*5%)^2+0.3(-2.5%)^2+0.4(2.5%)^2+0.2(5.5%)^2}

$$\sqrt { 0.1 ( - 14 \cdot 5 \% ) ^ { 2 } + 0.3 ( - 2.5 \% ) ^ { 2 } + 0.4 ( 2.5 \% ) ^ { 2 } + 0.2 ( 5.5 \% ) ^ { 2 } }$$

Aromātai

$$\frac{\sqrt{200170}}{2000}\approx 0.22370181$$

Ngā Upane Otinga

Whakahekea te hautanga \frac{5}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{0.1\left(-14\times \frac{1}{20}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakareatia te -14 ki te \frac{1}{20}, ka -\frac{7}{10}.

$$\sqrt{0.1\left(-\frac{7}{10}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tātaihia te -\frac{7}{10} mā te pū o 2, kia riro ko \frac{49}{100}.

$$\sqrt{0.1\times \frac{49}{100}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakareatia te 0.1 ki te \frac{49}{100}, ka \frac{49}{1000}.

$$\sqrt{\frac{49}{1000}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakarohaina te \frac{2.5}{100} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\sqrt{\frac{49}{1000}+0.3\left(-\frac{25}{1000}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakahekea te hautanga \frac{25}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\sqrt{\frac{49}{1000}+0.3\left(-\frac{1}{40}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tātaihia te -\frac{1}{40} mā te pū o 2, kia riro ko \frac{1}{1600}.

$$\sqrt{\frac{49}{1000}+0.3\times \frac{1}{1600}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakareatia te 0.3 ki te \frac{1}{1600}, ka \frac{3}{16000}.

$$\sqrt{\frac{49}{1000}+\frac{3}{16000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tāpirihia te \frac{49}{1000} ki te \frac{3}{16000}, ka \frac{787}{16000}.

$$\sqrt{\frac{787}{16000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakarohaina te \frac{2.5}{100} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\sqrt{\frac{787}{16000}+0.4\times \left(\frac{25}{1000}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakahekea te hautanga \frac{25}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\sqrt{\frac{787}{16000}+0.4\times \left(\frac{1}{40}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tātaihia te \frac{1}{40} mā te pū o 2, kia riro ko \frac{1}{1600}.

$$\sqrt{\frac{787}{16000}+0.4\times \frac{1}{1600}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakareatia te 0.4 ki te \frac{1}{1600}, ka \frac{1}{4000}.

$$\sqrt{\frac{787}{16000}+\frac{1}{4000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tāpirihia te \frac{787}{16000} ki te \frac{1}{4000}, ka \frac{791}{16000}.

$$\sqrt{\frac{791}{16000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakarohaina te \frac{5.5}{100} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\sqrt{\frac{791}{16000}+0.2\times \left(\frac{55}{1000}\right)^{2}}$$

Whakahekea te hautanga \frac{55}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\frac{791}{16000}+0.2\times \left(\frac{11}{200}\right)^{2}}$$

Tātaihia te \frac{11}{200} mā te pū o 2, kia riro ko \frac{121}{40000}.

$$\sqrt{\frac{791}{16000}+0.2\times \frac{121}{40000}}$$

Whakareatia te 0.2 ki te \frac{121}{40000}, ka \frac{121}{200000}.

$$\sqrt{\frac{791}{16000}+\frac{121}{200000}}$$

Tāpirihia te \frac{791}{16000} ki te \frac{121}{200000}, ka \frac{20017}{400000}.

$$\sqrt{\frac{20017}{400000}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{20017}{400000}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{20017}}{\sqrt{400000}}.

$$\frac{\sqrt{20017}}{\sqrt{400000}}$$

Tauwehea te 400000=200^{2}\times 10. Tuhia anō te pūtake rua o te hua \sqrt{200^{2}\times 10} hei hua o ngā pūtake rua \sqrt{200^{2}}\sqrt{10}. Tuhia te pūtakerua o te 200^{2}.

$$\frac{\sqrt{20017}}{200\sqrt{10}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{20017}}{200\sqrt{10}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{10}.

$$\frac{\sqrt{20017}\sqrt{10}}{200\left(\sqrt{10}\right)^{2}}$$

Ko te pūrua o \sqrt{10} ko 10.

$$\frac{\sqrt{20017}\sqrt{10}}{200\times 10}$$

Hei whakarea \sqrt{20017} me \sqrt{10}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{200170}}{200\times 10}$$

Whakareatia te 200 ki te 10, ka 2000.

$$\frac{\sqrt{200170}}{2000}$$